JAMRIS 2010 Vol 4 No 4

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JOURNAL of AUTOMATION, MOBILE ROBOTICS& INTELLIGENT SYSTEMS

All rights reserved © 1

Publisher:Industrial Research Institute for Automation and Measurements PIAP

If in doubt about the proper edition of contributions, please contact the Executive Editor. , excluding advertisements and descriptions of products.The Editor does not take the responsibility for contents of advertisements, inserts etc. The Editor reserves the right to make relevant revisions, abbreviations

and adjustments to the articles.

Articles are reviewed

H.J. Fraire Huacuja, J.L. González-Velarde,G. Castilla Valdez

A. Meléndez, O. Castillo, A. Alanis

Improving the intensification and diversificationbalance of the tabu solution for the RobustCapacitated International Sourcing problem (RoCIS)

Optimization of a reactive fuzzy logic controller for amobile robot using evolutionary algorithms

DEPARTMENTS

EVENTS

2

JOURNAL of AUTOMATION, MOBILE ROBOTICS& INTELLIGENT SYSTEMSVOLUME 4, N° 4, 2010

CONTENTS

REGULAR PAPER

Positive realizations of hybrid linear systemsdescribed by the general model using the statevariable diagram method

Motion prediction of moving objects in a robotnavigational environment using fuzzy-baseddecision tree approach

Control imrovement of shunt active power filterusing an optimized-PI controller based on ant colonyalgorithm and swarm optimization

Throwable tactical robot – description of constructionand performed tests

Recurrent neural identification and control ofa continuous bioprocess via first and secondorder learning

Novel genetic optimization of membership functionsof fuzzy logic for speed control of a direct currentmotor for hardware applications in FPGAs

V.S. Rajpurohit, M.M.M. Pai

B. Berbaoui, B. Ferdi, C. Benachaiba, R. Dehini

R. Czupryniak, M. Trojnacki

I. Baruch, C.-R. Mariaca-Gaspar

Y. Maldonado, O. Castillo, P. Melin

SPECIAL ISSUE SECTION

Hybrid Intelligent Systemsfor Control and Automation - Part I

Guest Editors: Oscar Castillo and Patricia Melin

T. Kaczorek

3

11

19

26

35

37

53

64

74

78

Abstract:

1. IntroductionIn positive systems inputs, state variables and out-

puts take only non-negative values. Examples of positivesystems are industrial processes involving chemical reac-tors, heat exchangers and distillation columns, storagesystems, compartmental systems, water and atmosphericpollution models. A variety of models having positive li-near behaviour can be found in engineering, manage-ment science, economics, social sciences, biology andmedicine, etc.

Positive linear systems are defined on cones and noton linear spaces. Therefore, the theory of positive sys-tems is more complicated and less advanced. An overviewof state of the art in positive systems theory is given inthe monographs [3], [4]. The realization problem forpositive discrete-time and continuous-time without andwith delays was considered in [1], [4-9], [15] and for po-sitive fractional linear systems in [13]. The reachability,controllability and minimum energy control of positivelinear systems with delays have been considered in [2].A new class of positive 2D hybrid linear systems describedby two vector equations has been introduced in [10] andof fractional positive hybrid systems in [11]. The reali-zation problem for positive linear hybrid systems hasbeen investigated in [12], [16], [17]. Structural decom-position of transfer matrix of positive normal hybridsystems has been proposed in [14].

In this paper a method for computation of positiverealizations of linear hybrid system described by the ge-neral model will be proposed.

The paper is organized as follows. In section 2 funda-mentals of positive hybrid linear systems are recalled andthe realization problem is formulated. The main result ispresented in section 3. In subsection 3.1 the proposedstate variable diagram method is presented for single-input single-output (SISO) linear hybrid systems. Anextension of the method for multi-input multi-output(MIMO) systems is presented in subsection 3.2.

The realization problem for linear hybrid systems des-cribed by the general model is formulated and solved. Suf-ficient conditions for the existence of positive realizationsare established. A procedure based on the state variablediagram method for computation of a positive realizationof a given transfer matrix is proposed. Effectiveness of theprocedure is demonstrated on two examples.

Keywords: positive realization, hybrid, general model,state variable diagram.

Concluding remarks are given in section 4.In the paper the following notation will be used. The

set of real matrices will be denoted by. The set of real matrices with nonnegative

entries will be denoted by and . Theidentity matrix will be denoted by and the

transpose will be denoted by .

Consider a hybrid linear system described by theequations [4]

(1a)

where

are the state, input and output vectors and

Boundary conditions for (1a) have the form

(2)

The hybrid system (1) is called internallypositive if andfor arbitrary boundary conditions

and any inputs

The transfer matrix of the hybrid system (1) isgiven by

where is the set of real matrices in andwith real coefficient.

[4] The hybrid system (1) is internallypositive if and only if

n m

IT

T s,z

s z

� �

� � �

� � �

��

� �

n m

n n

n m n n

p m

�

�

� �

�

n m

n

s,z p m

and

and

(1b)

(1c)

(3)

(4)

(5)

==

.

( )

1

1

n

2. Preliminaries and the problem formulation

.

( )

Definition 1.

Theorem 1.

POSITIVE REALIZATIONS OF HYBRID LINEAR SYSTEMS DESCRIBED BYTHE GENERAL MODEL USING THE STATE VARIABLE DIAGRAM METHOD

Tadeusz Kaczorek

Received 14 June 2010; accepted 12 July 2010th th

Journal of Automation, Mobile Robotics & Intelligent Systems VOLUME 4, N° 4 2010

Articles 3

+ + +

(6)

(7)

(8)

(9)

First we shall solve the problem for SISO hybrid sys-tems using the state variable diagram method [16].

Let a given transfer function of the SISO hybrid systemhave the form

where is the set of Metzler matrices (withnonnegative off-diagonal entries).

From (5) we have

since .

Knowing the matrix we can find the strictly positivetransfer matrix

The matrices (1c) satisfying the conditions(6), (7) and (5) are called the positive realization of thetransfer matrix .

The problem under considerations can be stated asfollows.

Given a rational matrix . Find itspositive realization, i.e. a realization (1c) satisfying theconditions (6) and (7).

In this paper sufficient conditions for the existenceof a positive realization will be established and a proce-dure for computation of a positive realization for a giventransfer matrix will be proposed.

M

D

T s,z

n n n

T s,z s,z

�

��

Definition 2.

( ) ( )p m�

( )

3. Problem solution

3.1. SISO systems

(10)

which by definition is the ratio of and forzero boundary conditions, where ,

and and are the zet and Lap-lace operators.

Using (8) and (9) we can find

(11)

and the strictly proper transfer function

(12)

where.

Multiplying the numerator and denominator of (12) bywe obtain

(13)

Defining

Y s,z U s,z( ) ( )

Journal of Automation, Mobile Robotics & Intelligent Systems

Articles4

VOLUME 4, N° 4 2010

Fig. 1. State variable diagram for transfer function (13).

(14)

From (14) and (13) we have

(15)

and

(16)

Using (15) and (16) we may draw the state variable diagram shown in Fig. 1.The number of integration elements is equal to and the number of delay elements is equal to . The outputs of

the integration elements are chosen as the state variables and the outputs of the delay elements as thestate variables . Using the state variable diagram we may write theequations

(17a)

(17b)

(17c)

where

(17d)

Substituting in the equations (17a) by and differentiating with respect to the equations (17b) we obtain theequations (1) with

(18a)

where

1/ 1/ 2

+1

s q z q

i i t

1 2


Articles 5

VOLUME 4, N° 4 2010

(18b)

There exists a positive realization (18) of the transfer function (10) if the following conditions are satisfied

1)2)

If the condition 2) is met then and the coefficients of the strictly proper transfer function (12) arenonnegative. From (18) it follows that if the conditions 1) and 2) are satisfied then

and by Theorem 1 the realization (18) is positive.From (18) we have the following corollary.

If the conditions 1) and 2) of Theorem 2 are satisfied then there exists a positive realization of the transferfunction (10) with and and .

Find a positive realization of the transfer function

(19)

Using (8) and (9) we obtain

(20)

and the strictly proper transfer function

(21)

In this case (15) and (16) have the form

(22)

and

(23)

Theorem 2.

Proof.

Corollary 1.

Example 1.

�

A B0 0= 0 = 0


Articles6

VOLUME 4, N° 4 2010

Using (22) and (23) we may draw the state variable diagram shown in Fig. 2.

The outputs of the integration elements are chosen as the state variables and the outputs of the delayselements as the state variables . From the state variable diagram we have the equations

(24)

and

(25)

The equations (24) and (25) can be written in the form (1), where

(26)

The desired positive realization of (19) is given by (20) and (26).

First we shall consider linear hybrid -inputs and one-output systems with the transfer matrix

(27)

where

(28)


x s,z x s,zx s,z x s,z

m

1 2

3 6

( ), ( )( ),..., ( )

3.2. MIMO systems


Articles 7

VOLUME 4, N° 4 2010


Articles8

It is assumed that the minimal common denominatorsatisfies the assumption

(29)

Using (8) and (9) we can find the matrix and thestrictly proper transfer matrix . Applying the ap-proach presented above for SISO systems to MIMO systemwith (27) we may find a realization of each transfer func-tion (28). A realization of the transfer function (27) canbe found by the use of the following theorem.

Let

(30)

be a realization of the transfer function (28). Then arealization of the strictly proper transfer matrix

(31)

is given by

(32)

Using (8), (31) and (32) we obtain

d s,z

DT s,z

( )

( )sp

Theorem 3.

Proof.

�

Theorem 4.

Proof.

Example 2.

There exists a positive realization (32) of thetransfer matrix (27) if all coefficients of the numerator

are nonnegative and all coefficient ofthe denominators are nonpositiveexcept the leading coefficient equal to 1.

If the assumptions are satisfied then by Theorem 2the realization (30) of the transfer function (27) is a posi-tive one. From (32) it follows that in this case all matrices(32) have nonnegative entries and by Theorem 1 the reali-zation of the transfer matrix is positive.

Given the transfer matrix

(33)

where is given by (19) and

(34)

Using (8) and (9) from (33), (19) and (34) we have

(35)

and

(36)

The state variable diagram corresponding to thetransfer function is shown in Fig. 2.and the positive realization is given by (26) i.e.

n s,z k md s,z k m

T s,z T s,z T s,z

T s,z

T s,z

k

k

sp

( ), = 1,…,( ), = 1,…,

( ) = [ ( ) ( )]

( )

( )

�

1 2

1

1

VOLUME 4, N° 4 2010



Articles 9

(37)

The state variable diagram corresponding tois shown in Fig. 3.

Using this state variable diagram we can write theequations

(38)

From those equations we have the realization ofin the form

(39)

The state variable diagram corresponding to the tran-sfer matrix (36) can be obtained as the connection of thestate variable diagrams shown in Fig. 2 and Fig. 3 (seeFig. 4).

T s,z

T s,z

sp

sp

2

2

( )

( )

Fig. 4. Connection of state variable diagrams.

By Theorem 3 the desired realization of the transfermatrix (33) is given by

(40)

where the submatrices are given by(37) and submatrices are given by(39). The realization is positive since all entries of thematrices (40) are nonnegative.

If the assumption (29) is not satisfied and

and

(41)

then to decrease the dimension of a realization of (27)it is recommended to find and write the transfermatrix (27) in the form

(42)

where denotes the degree of theminimal common denominator with respect to .

Note that the -inputs and -outputs systems can beconsidered as the sequence of -inputs and one-outputsystems. In this way the presented approach can be ex-tended for -inputs and -outputs linear systems.

The problem of computation of positive realizationsof hybrid linear systems described by the equations (1) bythe use of the state variable diagram method has beenaddressed. It has been shown that there exists a positiverealization of a given transfer matrix if all coefficients ofthe numerator of each transfer function are nonnegativeand all coefficients of the denominator are nonpositiveexcept the leading one equal to 1. The presented methodenable us to find a positive realization with zero ,matrices. If the condition (41) is satisfied then it is re-commended to find first minimal common denominatorfor each row of the transfer matrix. Those considerationscan be extended to linear hybrid systems with delays andto linear fractional hybrid systems.

A A B A CA A B A C

d s,z

deg d s,z deg d s,zs z

m pp m

m p

A B

11 12 11 12 1

21 22 21 22 2

0 0

, , , ,, , , ,

( )

( ) ( ( ))( )

Remark 1.

s z

4. Concluding remarks

VOLUME 4, N° 4 2010


Articles10

ACKNOWLEDGMENTS

AUTHORTadeusz Kaczorek

References

This work was supported by Ministry of Science and HigherEducation in Poland under work No NN514 1939 33.

[1]

- Professor at the Faculty of ElectricalEngineering, Bialystok University of Technology, Bialy-stok, Poland. E-mail: [email protected].

Benvenuti L., Farina L., “A tutorial on the positive reali-zation problem”, , vol. 49,no. 5, 2004, pp. 651-664.

[2] Busłowicz M., Kaczorek T., “Reachability and minimumenergy control of positive linear discrete-time systemswith one delay In:

, 6 -9 June, 2004, Kusadasi,Izmir, Turkey.

[3] Farina L., Rinaldi S.,, J. Wiley, New York, 2000.

[4] Kaczorek T.,London 2001.

[5] Kaczorek T., “Realization problem for positive discretetime systems with delay”, , vol. 30, no. 4,2004, pp. 117-130.

[6] Kaczorek T., “Positive minimal realizations for singulardiscrete-time systems with delays in state and control”,

, vol. 53, no. 3, 2005, pp.293-298.

[7] Kaczorek T., “A realization problem for positive conti-nuous-time linear systems with reduced numbers ofdelays”, , vol. 16, no. 3,2006, pp. 325-331.

[8] Kaczorek T., “Realization problem for positive multi-variable discrete-time linear systems with delays in thestate vector and inputs”, ,vol. 16, no. 2, 2006, pp. 101-106.

[9] Kaczorek T., “Positive minimal realizations for singulardiscrete-time systems with one delay in state and onedelay in control”, vol. 52,no. 3, 2005, pp. 293-298.

[10] Kaczorek T., “Positive 2D hybrid linear systems”,, vol. 55, no. 4, 2007, pp. 351-355.

[11] Kaczorek T., “Positive fractional 2D hybrid linear sys-tems”, , vol. 56, no. 3, 2008,pp. 273-277.

[12] Kaczorek T., “Realization problem for positive 2D hybridsystems”, , vol. 27, no. 3, 2008, pp. 613-623.

[13] Kaczorek T., “Realization problem for positive fractionaldiscrete-time linear systems”,

, vol. 3, 2008, pp. 76-86.[14] Kaczorek T., “Structural decomposition of transfer ma-

trix of positive normal hybrid systems”,, vol. 18, no. 4, 2008, pp. 399-413.

[15] Kaczorek T., Busłowicz M., “Minimal realization problemfor positive multivariable linear systems with delays”

, vol. 14, no. 2, pp. 181-187.[16] Kaczorek T., Sajewski Ł., “Computation of positive reali-

zations of MIMO hybrid linear systems with delays usingthe state variable diagram method”, ,

, IEEE Trans. Autom. Control

“. 12 Mediterranean Conference onControl and Automation

Positive Linear Systems; Theory andApplications

Positive 1D and 2D systems, Springer Verlag,

-System Science

Bull. Pol. Acad. Sci. Techn.

Int. J. Appl. Math. Comp. Sci.

Int. J. Appl. Math. Comp. Sci.

Bull. Pol. Acad. Sci. Techn.,

Bull.Pol. Acad. Sci. Techn.

Bull. Pol. Acad. Sci. Techn.

COMPEL

Int. J. Factory Autom.Robotics and Soft Comput.

Archive of Con-trol Sciences

,Int. J. Appl. Compt. Sci.

System Science

th

th th

vol. 34, no. 1, 2008, pp. 5-13.[17] Sajewski Ł., “Positive linear hybrid systems Realization

in the form of two-dimensional general model”,

(CD-ROM)

Auto-mation 2010, Pomiary Automatyka Robotyka 2/2010.

VOLUME 4, N° 4 2010

Abstract:

1. Introduction

In a dynamic robot navigation system the robot has toavoid both static and dynamic objects on its way to des-tination. Predicting the next instance position of a movingobject in a navigational environment is a critical issue as itinvolves uncertainty. This paper proposes a fuzzy rule-based motion prediction algorithm for predicting the nextinstance position of moving human motion patterns. Fuzzyrule base has been optimized by directional space approachand decision tree approach. The prediction algorithm istested for real-life bench- marked human motion data setsand compared with existing motion prediction techniques.Results of the study indicate that the performance ofthe predictor is comparable to the existing predictionmethods.

Keywords: short term motion prediction, fuzzy rule base,rule base optimization, fuzzy predictor algorithm, direc-tional space approach, decision tree approach.

For an autonomous mobile robot, performing a navi-gation-based task in an unknown environment to detectand avoid encountered obstacles is an important issue.It is also a key function for the robot body safety, as wellas for the task continuity. Generally, the architecture forthe vision-based robotic systems with the ability of ob-stacle detection and avoidance are relatively complica-ted. This may be attributed to the extraction of infor-mation from a stream of the site images consisting of thestatic and dynamic obstacles. In a dynamic robot naviga-tion system, the robot has to acquire the information onmoving objects and predict their future positions in orderto make path planning efficient. Short term object mo-tion prediction in a dynamic robot navigation environ-ment refers to the prediction of next instance position ofa moving object based on the previous history of itsmotion. The living beings and vehicles characterize thedynamic environment and exhibit motion in various di-rections with different velocities.

Real-life data often suffer from inaccurate readingsdue to environmental constraints, sensors, size of theobjects and possible change in motion pattern of themoving objects. This needs the system to be robust tohandle these uncertainties and predict next instanceobject position as accurate as possible within a shortduration. As a result, object motion prediction still con-tinues to be an active field of research. Research litera-ture has addressed solutions to the short term objectmotion predictions with different methods such as: curve

fitting or regression methods [7], [18], neural networkbased approaches [1], [2], [4], Hidden Markov stochasticmodels [19], Bayesian Occupancy Filters [5], ExtendedKalman Filter [9], [12], Stochastic prediction model [17],regression methods [18], [7] proposed in the literature,sample the positions of moving object at definite timeintervals, and fit the information to the regression equa-tion. With the current sampling positions, the regressionmodel predicts the position of the object for the nextsampling duration. The main drawback of this method isthe estimation of model coefficients in real-life environ-ment, which makes the system complex. Amalia Foka

[1],[2] have proposed a Polynomial Neural Network(PNN) architecture for object motion prediction. The PNNuses a second order polynomial equation as a transferfunction at each node. Training is done using evolutio-nary method. The algorithm needs huge amount of datasets for training and the performance of the algorithm ispoor in case of unseen datasets. Relative Error Back Pro-pagation neural network [4] for object motion predictionconsiders rectilinear motions of moving objects. Thealgorithm needs huge dataset for training and quality ofresults depend on the training data set used. Statisticalmethods for estimating obstacle locations using statis-tical features have been proposed such as Hidden MarkovModel [19] to predict object motion. The method is com-putationally intensive. The method proposed by R. Mad-havan [12] uses Extended Kalman Filter. Each pre-diction step is dependent on the previous sequence ofobservations made and the quality of prediction reduceswith increase in time and space horizon. C. Laugier and S.Petti [5] have proposed Baysean programming frameworkto predict the future position of moving object. The navi-gational environment is represented as a four dimensio-nal occupancy grid. The method is not suitable for largescale environment because of intrinsic complexity andnumerical computations. R. Irajit [15] in their workhave proposed a methodology based on Artificial Poten-tial Fields (APF) method which provides simple and effec-tive motion planners for practical path planning in fullydynamic environments. They have exploited the fuzzymodeling to define Fuzzy Artificial Potential Fields(FAPF) which provides a real-time and flexible path plan-ning. It is shown that FAPF paves a way to merge bothglobal and local path planning strategies. Simulationsshow that the planner is both very fast and capable ofhandling the local minima which can trap mobile robotsbefore reaching the goal. Based on the literature surveyon motion prediction models it is observed that i)Theexisting models lack flexibility in handling the uncer-tainties of the real-life situations; ii) Probabilistic

et al.

et al.

et al.

MOTION PREDICTION OF MOVING OBJECTS IN A ROBOT NAVIGATIONAL

ENVIRONMENT USING FUZZY-BASED DECISION TREE APPROACH

Vijay S. Rajpurohit, M.M. Manohara Pai

Received 10 ; accepted 5 July 2010th January 2010 th


Articles 11

models sometimes fail to model the real-life uncertain-ties; iii) The existing prediction techniques show poorresponse time due to their complex algorithmic structure;iv) Most of the approaches validate the results with simu-lated data or simple navigational environments.

The present work overcomes these difficulties witha novel solution for short term motion prediction usingfuzzy rule-based prediction technique. History of movingobject motion positions is captured in the form of fuzzyrule base, and the next instance object position is predic-ted using fuzzy inference process. Because of the multi-valued nature of fuzzy logic, this approach enjoys highrobustness in dealing with noisy and uncertain data.However, direct implementation of the rule base is notsuitable for real-life navigation systems due to the for-mation of huge number of rules. The total number offuzzy rules to be used are directly proportional to thenumber of fuzzy sets defined for the application and thenumber of fuzzy members present in each fuzzy set.Inconsistent and redundant rules identified in the rulebase are optimized by defining directional space withinnavigational space and decision tree approach.

The authors in their previous work [16] have imple-mented the extraction of objects of interest within therobotic navigational environment from the stereo visionsystem. Hence the focus of the present work is only limi-ted to the prediction of the moving object's motionwithin the navigational environment.

The paper is organized as follows. In section 2, fuzzyrule-based object motion prediction process is explained.Sections 3 and 4 discuss the optimization of the fuzzyrule-base using directional space approach and decisiontree approach.

In section 5 the fuzzy rule-base implementationdetails are presented. Experimental results are presentedin section 6. Finally, concluding remarks are given insection 7.

The difficulty of dynamic obstacle motion predictionlies on the uncertainty of obstacle motions. In the pro-posed work we have considered intentional motion modelfor the moving objects within the navigational environ-ment. Motion state of an obstacle at time is generallyrepresented by which represent the posi-tion, velocity and acceleration of the object at time . Inthis model an obstacle moves in a scheduled route, suchas a predetermined destination, or a programmed route.The obstacle may also try to avoid collision with others.In this case we have,

(1)

Where represents the variations in the accelera-tions resulting from any internal or external forces of theobstacle and are any two constants that specify thetendency of acceleration change. The function de-pends on the particular environmental conditions. It dif-fers from the random motion model in the way that,cannot be described by any probability distribution. Theacquisition of relies very much on the background

2. Fuzzy Rule-based Object motionprediction

tp v a

a t a t dt

e

a

( ( ), ( ), ( ))

( ) = ( ) +

( )

t t tt

e t

t

e t

e t

e t

� �

�

( )

( )

( )

( )

knowledge of the obstacles and a through observation ofthe history of motion of the moving objects. Fuzzy logicis an important branch of intelligent robotics. It does notneed to establish accurate mathematical models and it iseasy to construct its control structure with good robust-ness.

In the proposed work, the navigational environmentis modeled as a fuzzy world model. The robot is capable ofvisualizing the navigation environment in front (about180 degrees in semi circular range). Fuzzy regions infront of the robot are defined according to the visuali-zation capability of the sensors. Each object detected hasa distance variable from the Robot. This range data hasa different membership in each of the 7 range subsetsdefined as Very very far (VVFAR), Very far (VFAR), Far(FAR), Moderate (MOD), Near (NEAR), Very near (VNEAR),Very very near (VVNEAR). The direction of universe is divi-ded into 7 subsets. The linguistic variables that describethe angle heading are Very very left (VVLEFT), Very left(VLEFT), Left (LEFT), Front (FRONT), Right (RIGHT), Veryright (VRIGHT), Very very right (VVRIGHT). The fuzzy re-presentation of the environment is shown in Figure 1with numerical notation for each region. The fuzzy repre-sentation divides the whole navigation environment intodifferent regions like VVFAR-VLEFT (61), FAR-RIGHT(44)and NEAR-FRONT(23) etc.

As the regions defined are fuzzy in nature, there canbe overlaps from one region to another region. For sim-plicity these overlaps are not shown in the figure. Therange and angle information need to be represented bya suitable membership function. Many authors have ad-dressed critical issues relating to the selection and per-

Fig. 1. Division of Navigation Space into Fuzzy subsets ofRange and Direction.


Articles12

VOLUME 4, N° 4 2010

Fig. 2. Short term motion prediction.

3. Optimization of the Rulebaseby Partitioning the Navigational SpaceMany of the rules defined in the system look inconsis-

tent such as1. IF object at is VFAR,VVLEFT and object at is

FAR,VVLEFT THEN object predicted at isMOD,VVLEFT.

2. IF object at is VFAR,VVLEFT and object at isFAR,VVLEFT THEN object predicted at is FAR,VVLEFT.

Where the antecedents are same but the consequentsare different. The reason for the inconsistency is due tothe direction of traversal of the object. Future motion ofthe object is dependent on the history of the direction ofthe traversal of the object. To overcome this type of in-consistency, while defining the rule base, partitioning ofthe navigational space is done. Considering the naviga-tional space that is tessellated in eight geographical

t tt

t tt

1 23

1 23

Fig. 3. Division of navigational space into Directional Space.

formance of fuzzy membership functions for various real-time robot control applications [6], [8], [14]. In most ofthe cases triangular membership function has provedsuperior over other membership functions like trapezo-idal, Gaussian, bell shaped, polynomial-PI and sigmoidal.For our application as the prediction needs to be moreaccurate and the strength of the rule/ rules fired can ma-ke remarkable difference in the prediction, selection oftriangular membership function for representing angleand range values is inevitable. The selection of 07 fuzzysubsets for range and angle is moderate as selecting 05categories will have less number of fuzzy rules but, qua-lity of prediction may reduce if navigation space is large,selecting 09 or more number of categories will increasethe number of fuzzy rules as well as the complexity of thesystem which could reduce the response time of the pre-dictor. Both range and angle subsets are normalizedbetween 0-1.

In the rule base formation phase, rules are definedand added to the rule base using real-life data consistingof human motion patterns with velocity in the range 2-10kmph. At time , the position (angle and range) of themoving object from the robot is read. Using fuzzificationthe observed data is converted to fuzzy value. At time

and , where is threshold timedifference greater than or equal to 1 sec the sensor readsthe position of the same object. The reason for conside-ring 1 sec is that, the time needed to process thecaptured image to identify the objects of interest by thevision system needs at least 01 sec or more as per the cur-rent literature. The maximum value of the consideredwas 04 seconds. This is because, as the time gap betweenthe measurements increases the quality of the predictionreduces as well as the prediction looses its significance.The read value of the object position is converted to fuzzyvalue. The same process is followed at timeand to get the fuzzy value of the locationof the same object under observation. A fuzzy rule withthe positions of the moving object at time and asthe antecedent and the position of the object at timeas the consequent is formed and added to the rule-base.Each rule in the rule-base is represented as

and THEN

where and represent the range and the angle res-pectively of the object at time , and representthe range and the angle respectively of the object at time

, and and represent the range and the anglerespectively of the object at time . Similar rules are ad-ded to the rule-base for different objects observed atvarious positions in the navigation environment.

In the implementation phase of the predictor, the ro-bot observes the moving object at time and andsends the data to the fuzzy predictor algorithm. With theapplication of fuzzy inference process, prediction of thenext instance position of the moving object is carriedout. The complete process of short term motion predic-tion is represented in Figure 2.

t

t

t

R R R

1

2 ( 2 > 1 2 - t1 >)

3 ( 3 > 23 - 2 = 2 - 1)

IF ( 1, 1) ( 2, 2) ( 3, 3)

t t t

t tt t t t

t tt

Rt R

t Rt

t t

� �

� �

�

� � �

1 23

1 11 2 2

2 3 33

1 2

�

�

�


Articles 13

VOLUME 4, N° 4 2010

directions, the sensor readings of the object positions ta-ken at previous two time intervals forms a trajectory inone of these directions.

A separate directional space is created for each direc-tion (Figure 3) and rules are clustered based on the direc-tion of traversal object. Depending on the direction oftraversal of the object, only those rules which belong tothat directional space will be selected for processing.

The proposed fuzzy predictor algorithm has to processall the rules in a sequential form. The time complexity ofthe algorithm is linear and is of the order . This isreduced by reordering the rules in the form of a decisiontree. Each group of rules in the directional space is reor-ganized and IF-ELSE statements are written in the form ofa decision tree. The decision tree is a classifier in theform of a tree structure, where each node is either a leafnode - indicates the value of the target attribute (class)of examples or a decision node specifies some test to becarried out on a single attribute-value, with one branchand sub-tree for each possible outcome of the test.

Considering the basic organization of the fuzzy rule-base (which is a sequential set of rules) for two rules

Rule1: IF andIF THEN

Rule2: IF andIF THEN

We can have rulesi) starting with and and with any

values from 0-6ii) starting with and and and

with any values from 0-6iii) starting with and with

any values from 0-6iv) starting with and with

any values from 0-6

These set of rules when organized in sequential orderform a huge number of rules and consequently increasingthe size of the rule base for processing. Using decisiontree approach the two rules defined previously can bereorganized as follows.

{SW(d1),S(d2),SE(d3),E(d4),NE(d5),N(d6),NW(d7),W(d8)}

( )

((R1==2 , 1 == 2))((R2==1, 2 == 1)) R3, 3 = 21;((R1==2, 1 == 2))((R2==1, 2 == 2)) R3, 3 = 22;

R1=2 1, R2, 2

R1=2 1 = 2 R2 2

R1=2, 1 = 2, R2=1 2

R1=2, 1 = 2, R2=1, 2

1) if(R1==2)2) {3) if( 1 == 2)4) {5) if(R2==1)6) {7) if( 2 == 1)8) {R3, 3 = 21;}9) if( 2 == 2)10) {R3, 3 = 22; }11) }12) }13) }

4. Rulebase Optimization using Decisiontree Approach

O n

�

� �

�

� �

� �

� �

� �

� �

�

�

�

�

�

In the above expression if , no expression with-in the if block of is executed. Similarly all the rules inthe fuzzy rulebase can be reorganized in the form of a de-cision tree. For the developed rule-base, Figure 4 givesthe partial representation of the decision tree for IF-ELSEstatements. The input read by the fuzzy predictor algo-rithm classifies the input set to one of the directionalspaces (1 to 8) defined in Section 3. Each internal nodeis labeled with an integer 1 to 8 indicating the directionof traversal of the moving object and one of the direc-tions will be selected based on the history of object mo-tion. Each level in the decision tree corresponds to a fuz-zy set indicating either the range or direction subsets( ). Each item in the fuzzy antecedent is pro-cessed as and when it receives inputs at each level in thedecision tree and each input is a partial information ofthe position of the object in the navigational environ-ment. Each interior node in the decision tree correspondsto a variable; an arc to a child represents a possible valueof that variable. A leaf represents a possible value of tar-get variable given the values of the variables representedby the path from the root. Based on the input one of theoutgoing edges will be selected. The outgoing thick edgerepresents the selected fuzzy subset and remaining dot-ted edges represent the other unselected nodes.

To execute the algorithm, the process starts at theroot node , follows the edge labeled , and con-tinues recursively. Thus, the execution of the algorithmgives a path from the root to some leaf. Each leaf has aninteger label; when the execution reaches a leaf, its labelis returned as the algorithm's output.

Let be the length of the root-to-leaf path indecision tree traversed when the input is (rule). Thecomplexity of any decision tree algorithm is itsdepth and the complexity of the problem is the depthof the shallowest decision tree. For the prediction algo-rithm, the time complexity of the decision tree represen-tation of the rule-base system is given by

(2)

RR

v

R R

v f nv

T A, fA f

T A A

T n O n

1 21

1, 1, 2, 2

( )

( )

( )

( ) = ( )

�

� �

Fig. 4. Optimization of Fuzzy rule-base using Decision tree.


Articles14

VOLUME 4, N° 4 2010

where is the depth of the tree.

Table 1 represents the selection of the nodes of thedecision tree at various levels.

The rule-base implementation comprises of the obser-vation of the moving objects in the navigational environ-ment at equal time intervals and prediction of their futu-re position using the Fuzzy rule-base. This step involvesthe fuzzy inference process. The Fuzzy inference processcomprises five parts: fuzzification of the input data, ap-plication of the fuzzy operator (AND or OR) in the antece-dent, implication from the antecedent to the conse-quent, aggregation of the consequents across the rulesand defuzzification. The fuzzy inference process adoptedthe Mamdani model. The Mamdani model uses ruleswhose consequent part is a fuzzy set.

if is and is and isthen is (3)

where is the number of fuzzy rules,are the input variables, is the output vari-

able and and are fuzzy sets characterized by mem-bership functions and , respectively.

Given the inputs of the form

is is is

where are Fuzzy subsets of .The contribution of rule to Mamdani model's output isa Fuzzy set whose fuzzy membership function is compu-ted by

(4)

where ^ denotes the 'min' operator. The final output ofthe model is the aggregation of outputs from all the rulesusing the max operator.

n

Ri: x A x A x AY C i M

M x U js y V

Cx '

x A' , x A' , ... X A'

A' , A' , ... A' U , U , ... UR

' y x x x

Table 1. Decision Tree Analysis for Short Term MotionPrediction.

5. Fuzzy Rule-base Implementationfor Motion Prediction

1 1 2 2 3

1 2 1 2

1 1 2 2

= 1,2,3 ...

( = 1, 2,3 ... )

μ ( ) μ

1 1 2 2

μ ( ) = μ ' ( ) ' ( ) ... μ ' ( )}

i i is

i

j j

Aij i

Aij ij c i

r r

r r

i

c i A A A j j

�

�

μ

(5)

Defuzzification of the final output is done to get thecrisp value. Three most commonly used defuzzificationtechniques are considered: i) Fuzzy OR method/Min-Max,ii) Center Of Area (COA) and iii) Mean Of Maximum (MOM)methods. These methods operate on range and angleoutput subsets separately to generate the final crispvalue, indicating the range and angle of the final output.

Table 2 represents the evolution of the Fuzzy predic-tor algorithm. The table is parameterized by the stageof the algorithm development, the number of rules to beprocessed and the time complexity. The unoptimizedfuzzy predictor consists of all the rules identified duringthe formation of the rule-base. As the rule-base is largeand consists of inconsistent rules, its response time andrelative error is high. All the rules are processed in a line-ar order, the time complexity of the predictor iswhere is the number of rules. The directional spaceapproach clusters the rules in different directions whichreduces inconsistency, as well as response time. The de-cision tree approach reorganizes the rule-base and redu-ces the response time and time complexity of the predic-tor to where is the number of rules processedby the predictor algorithm. The fuzzy predictor algorithmis developed in C++ language.

The algorithm is tested on 1.66 GHz machine in VC++environment. The tests are carried out for real-life bench-marked datasets[3], [11], [13]. These data sets are gat-hered through i) INRIA Labs with data captured at INRIALabs at Grenoble, France (A wide angle camera lens in theentrance lobby of the INRIA Labs at Grenoble, France. Theresolution is half-resolution PAL standard); ii) MotionCapture Web group of Univ. of S. California (Consisting ofHuman Motion Patterns); iii) CMU Graphics Lab dataset.(Vicon motion capture system consisting of MX-40 came-ras with images of 4 megapixel resolution).

The data sets consist of different human motion pat-terns. These include people walking alone, running, me-eting with others, window shopping, entering and exi-ting shops (average speed in the range 2-10 kmph). Theposition of the moving objects within the navigational

μ ( ) = {μ '1 ( ), μ '2 ( ),….. μ ' ( )}

( )

( )

C C C C Ly max y y y

O nn

O logn' n'

6. Experimental Results

Table 2. Evolution of Short term predictor.


Articles 15

VOLUME 4, N° 4 2010

Level01

2

3

4

5

6

NodesDS={1,2,3,4,5,6,7,8}IF (R1 and 1)and (R2 and 2)R1={0,1,2,3,4,5,6}

1={0,1,2,3,4,5,6}

R2={0,1,2,3,4,5,6}

2={0,1,2,3,4,5,6}

R3={0,1,2,3,4,5,6}and3={0,1,2,3,4,5,6}

�

�

�

�

�

TypeDirectional SpaceRule Antecedent

Fuzzy Object distanceat time t1Fuzzy Object angleat time t1Fuzzy Object distanceat time t2Fuzzy Object angleat time t2Rule Consequent:Predicted FuzzyRegion at time t3

Development Stage

Basic UnoptimizeedFuzzy predictor

Predictor withDirectional SpaceApproach

Predictor withDecision TreeApproach

Number of Rulesto be processedin the Worst case1200

140 (Approx)

43(Approx)

Average TimeComplexity

O n n

O n' n'

n'< nO log n'

( )

( )

( )

whereis the numberof Fuzzy Rules

whereis the numberof Fuzzy Rulesand


Articles16

environment at any instant of time is given separately asa database so that any prediction algorithm can be testedand analyzed for any number of objects. These motionsexhibit intentional motion and predicting the next ins-tance position of objects in such scenario is an importanttask as it can find applications in keeping track of humanmotion patterns in hospitals, shopping complex and inexhibition halls etc.

Figure 5 represent the movement of the objects fromleft to right direction and the corresponding short termmotion prediction path. and represent the predic-ted and the actual path traversed by the moving object.

and represent the predicted goal and theactual goal of the object. is the actual path observedand is the actual goal reached by the object .

We define the Relative Error (RE) for sample testdata (sum of the number of predicted positions for a spe-cific object in motion) as

(6)

Where da is the actual position, is the predictedposition of the moving object in the navigational envi-ronment.

The average relative error is calculated for various testcases using Min Max, MOM and COA defuzzification tech-niques. For each test case the average response time isalso calculated to find its suitability to real-life environ-ment. For measuring the performance of the system thestandard parameters like prediction steps and relativeerror are used. The prediction algorithm is tested withprediction steps 02 seconds (Fig. 6), 03 seconds (Fig. 7),04 seconds (Fig. 8).

Table 3 represents the results of the Short term pre-dictor at various stages of development. Each stage inthe evolution of the fuzzy predictor is parameterized bythe relative error and average response time. These pre-diction steps indicate the in between time gap for eachsuccessive measurement (of the object position) by thevision system.

Variations in the velocity and directions of motion ofthe moving objects in these test cases are the sources ofuncertainty in predicting the next instance position ofthe moving object. Tests are carried out to measure therelative error between the actual and predicted positionswhen minute variations in velocity and directions of themoving objects are observed (Fig. 9).

The proposed predictor generates the next instance

Pi Ai

Pi G Ai GA

A G A

M

dp

( ) ( )1

1( ) 1

Fig. 5. Prediction graphs showing few of the path predic-tion solutions for Short term motion prediction.

position as a fuzzy region than as a (x,y) coordinate. Thishelps in the robot to classify the predicted region as adanger zone or the region of interest.

Defuzzification of the output generates the predictedcoordinate position of the moving object. The responsetime of the algorithm with Min Max defuzzification variedin the band from 1.45 milliseconds to 2.9 millisecondsand the relative error in the band from 0.04 to 0.4.

The response time of the algorithm with COA defuz-zification varied in the band from 3 milliseconds to 7 mil-liseconds and the relative error in the band from 0.01 to0.1. The response time of the algorithm with MOM defuz-zification varied in the band from 1.95 milliseconds to3.37 milliseconds and the relative error in the band from0.04 to 0.1. From the graphs it is observed that the pre-dictor with MOM defuzzification performs better in termsof response time with less relative error.

Fig. 6. Average response time and relative error of the Shortterm predictor at prediction step: 02 seconds.


VOLUME 4, N° 4 2010

RE = /M( )da dp�

da


Articles 17

Table 3. Results of Short term predictor at various stages ofdevelopment.


Fig. 9. Relative Error when measured with variations invelocity and direction of motion of moving objects.

Table 4. Comparison of Short term predictors.

A few of the well known motion prediction techniquesare re-implemented and are compared with the developedfuzzy predictor in respect of response time and relativeerror (Table 4). From the table it can be observed that theperformance of the predictor is comparable with regardto relative error but better than the other predictionmethods as far as response time is concerned.

In a dynamic navigation system the robot has toavoid stationary and moving objects to reach the finaldestination. Short term motion prediction for movingobjects in such an environment is a challenging problem.This paper proposes a simplified approach for predictingthe future position of a moving object (human motionpatterns) using fuzzy inference rules derived from expertsknowledge and real-life data. The rule-base has beenoptimized by directional space approach and decisiontree approach. Fuzzy based prediction is more flexible,can have more real life parameters, comparable to theexisting approaches and suited for real-life situations.The results of the study indicate that, the fuzzy predictoralgorithm gives comparable accuracy with quick responsetime when compared to existing techniques.

- Department of Computer Scienceand Engineering, Gogte Institute of Technology, Belga-um, 590008, India. E-mail: [email protected].

- Department of Information andCommunication Technology, Manipal Institute of Tech-nology, Manipal, 576104,India.E-mail: [email protected].* Corresponding author

7. Conclusion

ACKNOWLEDGMENTS

AUTHORSVijay S. Rajpurohit*

M.M. Manohara Pai

References

The authors are thankful to the benchmark dataset provided byEC Funded CAVIAR project, CMU Graphics lab and Motion cap-ture web group. We are indebted to AICTE, Government of India,for funding our project.

[1] Foka Amalia, Trahanias Panos E., “Predictive Autono-mous Robot navigation”. In:

, EFPL,Lausanne, Switzerland, Oct. 2002, pp. 490-494.

[2] Foka Amalia, Trahanias Panos E., “Predictive control of

IEEE/RSJ InternationalConference on Intelligent Robots and Systems

VOLUME 4, N° 4 2010

Development Stage

Basic UnoptimizedFuzzy predictorPredictor withDirectionalSpace ApproachPredictor withDecision TreeApproach

Relative Error

1-20%

1-15%

1-10%

Average Responsetime in millisec500

15-20

2-5

Short TermPredictorNeural Networkpredictor[8]Bayesian OccupancyFilters[10]Extended KalmanFilter[12]Fuzzy Predictorwith MOM

Relative Error

6-17%

1-10%

1-20%

1-10%

Response timein seconds560x 10 sec

100x 10 sec

0.1 sec

02x 10 sec to05x 10 sec

-3

-3

-3


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Robot velocity to avoid objects in dynamic environ-ments” In:

, 27 -31 October, 2003, LasVegas, Nevada, pp. 370-375.

[3] Gardner Andrew, Pighin Fred, 2001, ,Retrieved July 2008, from University of SouthernCalifornia websitehttp://projects.ict.usc.edu/graphics/animWeb/humanoid/.

[4] Chang Charles C., Song Kai-Taj, “Dynamic motion plan-ning based on Real-Time object Prediction” In:

, Minnesota, USA.[5] Laugier C., Petti S., “Navigation in Open and Dynamic

Environments” In, 2005, Barcelona,

Spain.[6] Huang Hong, Chang Liuchen, “Simulation study on the

membership functions of the basic logic controller forthe electric vehicle propulsion systems”. In:

Cal-gary, Canada, May 1996, pp. 1004-1007.

[7] Yu Huiming, Su Tong, “A Destination Driven Navigatorwith Dynamic Object Motion Prediction”. In:

Seoul, Korea.21 -26 May, 2001, pp. 2692-2697.

[8] Zhao Jin, Bose Bimal K., “Evaluation of membershipfunctions for fuzzy logic controlled induction motordrive”.

volume 1, 2002, pp. 229-234.[9] Kalman R., “A New Approach to Linear Filtering and

Prediction Problem”,vol. 82, 1960, pp. 35-45.

[10] Webb P., Fayad C., Brettenbatch C., “The integrationof an optimized Fuzzy logic navigation algorithm intoa semi-autonomous Robot Control System” In:

,Leicester, UK, 29 June 2000.

[11] , Retrieved July 2008 from Car-negie Mellon University Motion Capture Database web-site: http://mocap.cs.cmu.edu/, funding from NSFEIA-0196217.

[12] Madhavan R., Schlenoff C.,. SPIE Aerosense confe-

rence, Orlando, 21 -25 April, 2003.[13] Fisher Robert, Santos-Victor Jose, James Crowley

(2001), , RetrievedJan 2008,fromhttp://homepages.inf.ed.ac.uk/rbf/CAVIAR/, funded by EC Funded CAVIAR project/IST 200137540.

[14] Berkan Riza C., Trubatch Sheldon L.,

John Wiley & Sons Inc., 1997.[15] Irajit R., Manzuri-Shalmanit M. T., “A New Fuzzy-Based

Spatial Model for Robot Navigation among DynamicObstacles”. In:

, Guangzhou, China, 30 May - 1 une,2007, pp. 1323-1328.

[16] Rajpurohit Vijay S., Pai Manohara M. M., “Feature Ex-traction Learning For Ster Naviga-tion System”. In:

,pp. 362-365, ISBN-1-4244-0715-X, NITK, Surathkal,

. IEEE/RSJ International Conference on Intel-ligent Robots and Systems

Motion Capture Web

. Pro-ceedings of the 1996 IEEE Intl. Conference on Roboticsand Automation

. : IEEE International Conference onRobotics and Automation (ICRA'05)

CanadianConference on Electrical and Computer Engineering,

Internatio-nal Conference on Robotics 2L Automation,

IECON Proceedings (Industrial Electronics Confe-rence),

Transactions of the ASME-Journalof Basic Engineering,

. Interna-tional Workshop on Recent Advances in Mobile Robots

Motion Capture Database

Moving Object Prediction forOff-road Autonomous Navigation

CAVIAR Video Sequence Ground Truth

Fuzzy SystemsDesign Principles: Building Fuzzy If-Then Rule Bases.

IEEE International Conference on Controland Automation

eovision Based Robot14 IEEE International Conference on

Advanced Computing Communications - ADCOM 2006

th st

st th

th

st th

th st

th

Mangalore, 20 -23 , December 2006.[17] Nam Yun Seok, Lee Bum Hee, Kim Moon Sang, “View-

Time Based Moving Object Avoidance using StochasticPrediction of Object Motion”. In:

, Minneapolis,Minnesota, USA, April 1996.

[18] Hui-Zhong Zhuang, Du Shu-Xin, Wu Tie-jun, “On-linereal-time path planning of mobile Robots in dynamicuncertain environment”.

, 2006, pp. 516-524.[19] Zhu Q., “Hidden Markov Model for Dynamic Object Avo-

idance of Mobile Robot Navigation”,, 1991, pp. 390-396.

th rd

IEEE InternationalConference on Robotics and Automation

Journal of Zheing UniversityScience A

IEEE Transactionson Robotics and Automation

VOLUME 4, N° 4 2010

Abstract:

1. IntroductionThe advancements of electronic devices technology

and its use in the industry has produced harmonic in linedistribution network [1]. In order to eliminate thesestroubles, researchers has proposed new technique to eliminate theses harmonics. One of the theories is the instantaneous power theory (p-q theory). This theory wasintroduced by Akagi, Kanazawa and Nabae in 1983 [2] inJapanese.

By tradition, passives filters have been used to eliminate the current harmonic distortion and compensate thereactive power, but can resonate with supply impedance.

The correct implantation of PI controller DC link voltage of (SAPF) depends two parameters proportinnal gain

and integral gain which are tuned by trial anderror. In the other hand has a problem in the time neededto accomplish this task.

To trounce this problem many methods have been developed, such as Ziegler-Nichols [3].

An improvement in tuning can be achieved using optimization techniques, and in particular those based onartificial intelligence.

In this paper, we formulate the problem of design DClink voltage PI controller as an optimization problem. Theproblem formulation adopts three performances indexes,the maximum overshoot, the rise time and the integralabsolute error of step response as the objective functionto determine the PI control parameters for getting a wellperformance under a given system, the primary designgoal is to obtain good load disturbance response by mini

In the last years, there has been a increase currentsharmonics on electrical network injected by nonlinearloads, such as rectifier equipment used in telecommuni-cation system, power suppliers, domestic appliances, ect.

This paper makes a comparison of the effectiveness ofthe two methods on particular optimization problem,namely.

The tuning of the parameters for PI DC link voltage toa shunt active power filter. The simulation results demon-strates that the optimized PI controller by ant colony(ACO) presents a advantage of little response time and bestcontrol performances compared to the optimized PI withParticle swarm (PSO). This comparison is shown on reducing harmonic current supply (THD).

-

ant colony optimization, particle swarm optimization, shunt active power filter, harmonic compensation, PI controller.

Keywords: --

--

-

-

-

-

-

( ) ( )K Kp i

mizing the integral absolute control error. At the sametime, the transient response is assured by minimizing theothers three performance indexes.

Two approach methods has been used to show itsimpact on SAPF the ant colony algorithm and particleswarm algorithm

The main idea of ACO is to model the problem as thesearch for a minimum cost path in a graph that base theevolutionary meta-heuristic algorithm. The behavior ofartificial ants is inspired from real ants. They lay pheromone trails and choose their path using transition probability. Ants prefer to move to nodes which are connectedby short edges with a high among of pheromone. Thealgorithm has solved traveling salesman problem (TSP),quadratic assignment problem (QAP) and job-shop scheduling problem (JSSP) and so on [4]-[5].

The problem must be mapped into a weighted graph,so the ants can cover the problem to find a solution. Theants are driven by a probability rule to choose theirsolution to the problem (called a tour). The probabilityrule (called Pseudo-Random-Proportional Action ChoiceRule) between two nodes and .

(1)

The heuristic factor or visibility is related to thespecific problem as the inverse of the cost function. Thisfactor does not change during algorithm execution; instead the metaheuristic factor (related to pheromonewhich has an initial value ) is updated after each iteration. The parameters and enable the user to direct thealgorithm search in favor of the heuristic or the pheromone factor. These two factors are dedicated to everyedge between two nodes and weight the solution graph.

The pheromones are updated after a tour is built, intwo ways: firstly, the pheromones are subject to an evaporation factor , which allows the ants to forget theirpast and avoid being trapped in a local minimum (equation 2). Secondly, they are updated in relation to thequality of their tour (equations 3 and 4), where the quality is linked to the cost function.

(2)

(3)

(4)

.

--

-

-

-

-

-

-

-

2. Ant colony optimization

i j

�

�

�

� �

�

ij

ij

0

( )

CONTROL IMROVEMENT OF SHUNT ACTIVE POWER FILTER USINGAN OPTIMIZED-PI CONTROLLER BASED

ON ANT COLONY ALGORITHM AND SWARM OPTIMIZATION

Brahim Berbaoui, Brahim Ferdi, Chellali Benachaiba, Rachid Dehini

Received 6 February 2010; accepted 26th th July 2010


Articles 19

belong

otherwise

Where is the number of ants, represents the edges ofthe solution graph, and is the cost function of tour ,built by the ant.

m LTC

k

-

-

Pbest -

-gbest

i.th xi =xi xi xid

i.th -

Pbest = Pbest , Pbest , ..., Pbest

gbest i -vi vi vi vid

Pbest gbest

v = wv c rand Pbest x c randgbest x

x = x v

i nm d

ndtv i twc crandv iPbest i.thGbest

k k

th

i i i id

d

id d

i,m i,m i,m i,m

m i,m

i,m i,m i,m

i,m

i,d

i

3. Particle swarm optimizationParticle swarm optimization (PSO) is a population ba-

sed stochastic optimization technique inspired by socialbehavior of bird flocking or fish schooling [6]. PSO learnsfrom the scenario and uses it to solve the optimizationproblems. In PSO, each single solution is a "bird" in thesearch space.

We call it "particle". All particles have fitness valueswhich are evaluated by the fitness function to be opti-mized, and have velocities which direct the flying of theparticles. The particles fly through the problem space byfollowing the current optimum particles.

PSO is initialized with a group of random particles(solutions) and then searches for optima by updating generations. In each iteration, every particle is updated byfollowing two "best" values. The first one is the best solution (fitness) it has achieved so far. (The fitness value isalso stored.) This value is called . Another "best" value that is tracked by the particle swarm optimizer is thebest value, obtained so far by any particle in the population. This best value is a global best and called .

For example, the particle is represented asin the d-dimensional space. The best

previous position of the particle is recorded and represented as:

(5)

The index of best particle among all of the particles inthe group is . The velocity for particle is represented as .

The modified velocity and position of each particlecan be calculated using the current velocity and the dis-tance from to as shown in the followingformulas [8].

(6)-(7)

Where:- Number of particles in the group,- Dimension,- Pointer of iterations (generations),- Velocity of particle at iteration ,- Inertia weight factor,

, - Acceleration constant,- Random number between 0 and 1,- Current position of particle at iterations,- Best previous position of the particle,- Best particle among all the particles in thepopulation.

( 1, 2, ..., )

( )

= ( 1, 2, ..., )

()( ) ()( )

= 1,2,..., ;= 1,2,..., ;

()

1 2

1 2

1 2

� � �

�

�

4. Organization of objective function

5. Configuration of shunt active power filter

In this work, the optimized parameters objects areproportional gain and integral gain , the transferfunction of PI controller is defined by:

(8)

The gains and of PI controller are generated bythe ACO and PSO algorithm for a given plant. As shownin Fig. 1. The output u(t) of PI controller is given by(equation 9):

(9)

For a given plant, the problem of designing a PI controller is to adjust the parameters and for gettinga desired performance of the considered system. Both theamplitude and time duration of the transient responsemust be kept within tolerable or prescribed limits, for thiscondition, three key indexes performance of the transient response are utilized to characterize the performance of PI control system. These key indexes maximumovershoot, rise time and integral absolute control errorare adopted to create objective function which is definedas:

(10)

The maximum overshoot is defined as:

(11)

characterize the maximum value of and de-note the steady-state value of .

For represent the function of the rise time is defi-ned as the time required for the step response.

In the other hand, the integral of the absolute magni-tude of control error is written as:

(12)

The most important objective of the APF is to com-pensate the harmonic currents due to the non linear load.Exactly to sense the load currents and extracts the har-monic component of the load current to produce a refe-rence current Ir as shown in Fig. 2, The reference currentconsists of the harmonic components of the load currentwhich the active filter must supply [7].

K K

K K

-K K

--

y y yy

y

p i

p i

p i

max ss

rt

Fig.1. PI control system.


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VOLUME 4, N° 4 2010

( 1)t�

( 1)t�

( )t

( )t

( 1)t�

( )t

( )t

t

( )t

)(sGs

)(ty

PSO

ACO _

)(sGp

)(te)(tr )(tu

(15)

The harmonic component of the total power can beextracted as:

(16)

Where,: The DC component

: Harmonic component

Similarly,

(17)

Finally, we can calculate reference current as:

(18)

Here,

(19)

In this paper, we present the SAPF as controlledplant, the SAPF diagram is shown in Fig. 3.

ACO-PSO

The estimation of the reference currents from themeasured DC bus voltage is the basic idea behind the PIcontroller based operation of the SAF. The capacitor vol-tage is compared with its reference value in order tomaintain the energy stored in the capacitor constant.

p

p

v

L

L

da

7. ACO and PSO applied to optimize PIparameters of dc-link capacitor

Fig. 3. Control diagram of APF system.

*

This reference current is fed through a controller andthen the switching signal is generated to switch the po-wer switching devices of the active filter such that theactive filter will indeed produce the harmonics requiredby the load. Finally, the AC supply will only need to pro-vide the fundamental component for the load, resultingin a low harmonic sinusoidal supply.

The identification theory that we have used on shuntAPF is known as instantaneous power theory, or PQtheory.

It is based on instantaneous values in three-phasepower systems with or without neutral wire, and is validfor steady-state or transitory operations, as well as forgeneric voltage and current waveforms.

Vector of tension: andVector of current: and

The PQ theory consists of an algebraic transformation(Clarke transformation) of the three phase voltages andcurrent in the abc coordinates to the coordinates [8].

(13)

(14)

The instantaneous power is calculated as:

Fig. 2. Equivalent schematic of shunt APF.

6. Instantaneous active and reactive p-qpower theory

Inputs:v t , v t v ti t , i t i t

a b c

a b c

( ) ( ) ( )( ) ( ) ( )

��


Articles 21

VOLUME 4, N° 4 2010

ref currentgenerator

CurrentDetection

ControlCircuit

Converter

Load

The DC link voltage discretely at the positive zero-cro-ssing point of respective phase source voltage, computesthe variation of power according to difference of DC linkvoltage between two sampling points. The regulation ofthe error between the capacitor voltage and its referenceis assured by The PI controller which its output is mul-tiplied by the mains voltage waveform , , in or-der to obtain the supply reference currents.

The equivalent schematic diagram of system which isused to maintain the DC link voltage constantly is shownin Fig.4.

In this work, the objective of an optimal design of PIcontroller DC-Link for given plant is to find a best para-meters and of PI control system such that the per-formance indexes on the transient response is minimum.

For ACO approach, each parameter of and is hin-ted by 100 nodes respectively and there is resolution0.0001 among each node, one node represents a solutionvalue of parameters and . Thus, the more accuracytrails are updated after having constructed a completepath and the solution found.

For PSO approach, the evolution procedure of PSOAlgorithms is presented as follow Fig. 5. Producing initialpopulations is the first step of PSO. The population iscomposed of the chromosomes that are real codes. Thecorresponding evaluation of a population is the “fitnessfunction” which is the performance index of apopulation.

The fitness value is bigger, and the performance isbetter. After the fitness function has been calculated, thefitness value and the number of the generation deter-mine whether or not the evolution procedure is stopped(Maximum iteration number reached?). After this, calcu-late the of each particle and of population(the best movement of all particles). The update thevelocity, position, and of particles give a newbest position.

In this work, we have used the following parametersvalues for the ant colony optimization which is step inthe Table 1.

V V V

K K

K K

K K

Pbest Gbest

gbest Pbest

s s s

p i

p i

p i

id

1 2 3

Fig. 4. Equivalent schematic diagram system.

8. Design of optimizing algorithm

Table 1. Initial values parameters of ACO.

Table 2. Parameters of PSO algorithm.

Table 3. SAPF parameters

Ant Number 20Maximum Cycle Time 100Initial Value of Nodes Trail Intensity 0.1Coefficient 0.6Relative Important Parameter of Trail Intensity 3Relative Important Parameter of Visibility 2

And for the particle swarm the parameters values arepresented Table 2.

Population Size 60Number of Iterations 150

max 0.7min 0.1

1.5Min-offset 200

The proposed PI controller of DC link capacitor desig-ned by ACO and PSO on filtering system that was set inMatlab Simulink environment to predict performance ofthe proposed method. The SAPF model parameters areshown in the following Table 3.

.

Supply phase voltage 220 VSupply frequency 50 HzFilter inductor 1mH

link capacitor 4.4 mFSmoothing inductor 0.1 mHSample time 4 μs

A number of simulation results were developed withdifferent cases. The SAPF is connected in parallel withnonlinear load, the first case is the PI-classical using onthe system to allow us to see the regulation of DC link vol-tage and its effect for damping harmonics current and re-ducing total harmonic distortion (THD). For the secondcase the proposed optimized PI-controller with ACO andPSO has been introduced in order to improve a SAPF per-formance and meet the requirements of harmonic elimi-nation and reactive compensation.

In the conventional PI controller the parametersand has been determined by classical method which isZiegler-Nichols method for tuning PI controller. This pro-cedure is now accepted as standard in control system andis based on plant step responses.

The method used in this work known as the continu-ous cycling which integration and derivative terms of thecontroller are disabled and the proportional gain is in-creased until a continuous oscillation. Consideringand its related oscillating period , the PI parameterscan be calculated from the following equation:

�

�

�

wwc = c

Ufs

LfDc Cf

Ts

KK

KuTu

1 2

9. Simulation result

10. A Case of classical PI-controllerp

i


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VOLUME 4, N° 4 2010

ref currentgenerator

Converter

Load

(20)

The PI control scheme involves regulation of the dclink voltage to set the amplitude of reference current forharmonic and reactive power compensation [9], [10]. Inthis study, we have simulated only the network supplyconnected on the nonlinear load, the total harmonic dis-tortion found is 20.90 % which indicate the harmonicpresence in the current source caused by nonlinear load.In the first case, the SAPF has been introduced in order tocompensate these harmonics and has reduced the THDfrom 20.90% to 0.99%. The results founded are shown inthe following figures.

Harmonic supply current components

Fig. 6. Load current waveform

Table 4. Harmonic supply current phase-a-component withtraditional PI controller method.

Table. 5. THD results.

Fig. 7. Injected current waveform.

Fig. 8. DC link voltage waveform.

Fig. 9. Harmonic spectrum of supply current.

11. B Case of optimized PI-controllerIn the second case, the shunt active power filter was

examined using optimized PI - controller DC link voltage,the optimal parameters has been determined by using antcolony optimization (ACO) and particle swarm optimiza-tion (PSO). The main objective is to minimize the fitness


Articles 23

VOLUME 4, N° 4 2010

N571113171923252931353741434749

THD

Isa(n)/Isa(1) [%]0.180.340.240.210.210.170.180.130.160.110.120.110.120.100.110.100.99

THD (%)i

Withoutfiltering

20.90

FSAPF filteringwith classical

PI DC link voltage0.99

Robustness

3.90


Articles24

function that is defined by the equation (10).In this paper, we have based on the minimizing inte-

gral absolute error, so it has been multiplied by coeffi-cient . The objective function is returned by the fol-lowing equation:

(21)

In this case, we have fixed value: and thatto give an importance for the integral error in formula-tion function. Simulation studies are carried out to pre-dict performance of the proposed method. The Fig. 10shows the DC link voltage response curves of system usedprimal PI parameters and optimized PI parameters, andthe value of system indexes are compared in Tab. 5. Thesource voltage, current, load current, harmonic order and

link voltage waveforms are shown in the followingfigures after adopted the optimized system.

In Fig. 10, the stability convergence and robustness.Hence, the high performance can be achieved.

The results we obtained demonstrate that a low THDvalue can be reached by using the optimized system stu-died in this paper.

The current source represented by Fig. 12 takes thesinusoidal form, as well as the spectral analysis Table 6shows the absence of the more share of the harmonicsrows which implies the good performances of the opti-mized PI-controller compared with classical PI.

�

� � = 2.5

Dc

Table. 5 comparisons of SAPF indexes between used andunused ant colony algorithm and particle swarm algorithm.

Fig. 10. DC link voltage response curve of SAPF used antcolony optimization and particle swarm optimization.

Table 6. Harmonic supply current phase-a-component withoptimized PI controller methods.

Fig. 11. Source voltage waveform.

Fig. 12 Supply current waveform of single phase.

Harmonic supply current components

.

VOLUME 4, N° 4 2010

Parameterand indexes

Proportional gainIntegral gainOvershoot (%)Rise time (sec)

Integralabsolute error

PI nonoptimized

1201.0585.660.0009

1.0182e+001

PIwith ACO

1900.000488.52

0.0008696.8543e+000

PIwith PSO

1800.0002887.99

0.000877.0013e+000

N

571113171923252931353741434749

THD

Isa(n)/Isa(1) [%]using ACO

0.130.330.200.200.190.150.170.110.140.090.110.090.100.090.090.090.91

Isa(n)/Isa(1) [%]using PSO

0.140.330.210.210.190.150.180.110.150.090.110.090.100.090.100.100.93


Articles 25

Table 7. THD results.

In this paper we have presented a comparative bet-ween two optimization approach ant algorithm andswarm algorithm for design PI controller DC link voltageof SAPF.

The PI-ACO control method has improved the activepower filter performance compared with PI-PSO and tra-ditional PI controller, and it can be seen in the Supplycurrent filtering result Fig. 12.

The deformations have been clearly reduced and alsothe harmonic distortion has been decreased comparedwith the SAPF filtering using traditional PI controller me-thod, so this comparison can been shown in the followingfigure.

According to the results of the computer simulations,the optimized PI using ACO is better than the traditionalPI and also PI with PSO.

The PI with ACO algorithm is the best controller whichpresents satisfactory performances, less overshoot andminimal rise time compared with classical PI and opti-mized PI with PSO.

Furthermore, results has demonstrated that thecontrol strategy with ACO for DC link voltage is efficientfor compensating the current harmonics, and the propo-sed system has reduced the THD with 8 % less than primalsystem and 2% less than system using particle swarmoptimization ( SAPF without ACO ) as shown in Fig. 13.So we can say that the PI-ACO is the best controller whichpresented satisfactory performance and good robustness.

12. C Comparative Study

13. Conclusion

ACKNOWLEDGMENTSThis work was supported by the AGH University of Science andTechnology under Grant No. 11.11.120.612.

AUTHORS*

References

- Department of Electrical Engineering,Bechar University, B.P 417 BECHAR (08000), Algeria.Email: [email protected].* Corresponding author

[1]

Brahim Berbaoui , Brahim Ferdi, Chellali Benachaiba,Rachid Dehini

Fang Zheng Peng, ”Application Issues of Active PowerFilters” , 1998.

[2] Akagi H., Kanazawa Y., Nabae A., "Generalized Theoryof Instantaneous Reactive Power and Its Applications"Transactions of the IEE-Japan, Part B, vol. 103, no.7,1983, pp. 483-490. (in Japanese)

[3] Ziegler J.G., Nichols N.B., „Optimum settlings for auto-matic controllers” , Vol. 64, 1942,pp. 759-768.

[4] Dorigo M., Gambardella L.M., “Ant Colony System:A Cooperation Learning Approach to the Traveling Sa-lesman Problem”. IEEE Trans. Evolutionary Computa-tion, vol. 1, no. 1, 1997, pp. 53-66.

[5] Maniezzo V., Colorni A., “The Ant System Applied to theQuadratic Assignment Problem”. IEEE Transactions onKnowledge and Data Engineering, vol. 11, issue 5,1999, pp. 769-778.

[6] Kennedy J., Eberhart R.C., “Particle Swarm Optimiza-tion”. In:

1995,pp. 1942-8.

[7] Wada K., Fujita H., Akagi H., “Considerations of a ShuntActive Filter Based on on Voltage Detection for Instal-lation on a Long Distribution Feeder'. In:

, 2001, pp. 157-163.[8] Akagi H., Kanazawa Y., Nabae A., Generalized Theory

of the lnrtrntansour Reactive Power in Three-Phssc Cir-cuirs . In: -

, Tokyo, 1983, pp. 1375-1186.[9] Gu J.J., Xu D.G., “Active power filters technology and

its development”, , vol. 7,no. 2, 2003, pp. 126-132.

[10] Jou H.L., Wu J.C., Chu H.Y., “New single-phase activepower filter” ,vol. 141, no. 3, May 1994, pp. 129 134.

IEEE Industry Application Magazine

ASME Transactions

Proceedings of the 1995 IEEE internationalconference on neural networks, vol. 4. Piscataway, NJ:Inst. of Electrical and Electronics Engineers;

Proc. Conf.IEEE-IAS Ann. Meeting

Proc. IPEC Tokyo '93 Int. CO Power Electronics

Electric Machines And Control

Proc. Inst. Elect. Eng., Electr. Power Appl.

.

.

.

”

”

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VOLUME 4, N° 4 2010

THD(%)

i

Withoutfiltering

20.90

SAPF usingoptimized PI

with PSO0.93

SAPF usingoptimized PI

with ACO0.91

Robustness

4.25/ACO4.09/PSO

Fig. 13. Comparative harmonic spectrum of supply current for both with classical PI, PI-AO and PI-PSO.

Abstract:

1. IntroductionAccording to increasing rate of terror acts the cha-

racter and methods of setting up explosive charges haschanged. Therefore, there appeared a need to changeconception, construction and the scale of pyrotechnic ro-bots and even their tasks. In the last years a bigger em-phasis was placed on development of small robots whichpurpose is not neutralization but acquiring information.Thanks to acquiring significant information, the servicesare able to react adequatly to the incident. The role ofsmall robots is and will be to perform preliminary recon-naissance of incident place, acquiring information forintervention squads in open or secret manner. The othervital attribute of small robots is their independent workas information sources, tracing and simple neutralizationmachines. The main advantage should be the possibility

This paper concerns a throwable tactical robot (TTR) forspecial purposes. The necessity of use of that kind of robotsand the existing design solutions are discussed. There arealso described construction, parameters, and principles ofoperation of the robot and the control panel, as well as theconducted robot tests.

Keywords: throwable robot, special robot, teleoperation.

to reach every target virtually unnoticeably either in acombat mission or rescue action. Their small sizes shouldassure secrecy and possibility of free penetration of verysmall spaces. [1], [2], [5]

The review of existing design solutions shows themost desired direction of development of this kind ofrobots for active teleobservation and tracing. The maincharacteristics which small robots should have is the pos-sibility to place them by hand throwing at the operator'sinterest area. That is in the simplest and fastest way,decreasing the danger to indispensable minimum, allo-wing to penetrate spaces inaccessible for the operator,i.e. beyond an obstacle. [1], [2]

Nowadays we can find information about differentcommercial and non-commercial solutions of throwablerobots. One of non-commercial robots of this kind is therobot presented in the Figure 1. It consists of two modu-les connected with each other by a common driven axis.It has also 4 balls (Omni-Ball) positioned at the end ofmodules that have one active and two passive axes ofrotation. Such a solution of the robot construction en-ables both its moving, in a collapsed form, in narrowareas using balls drive, and moving, for instance, in de-bris area using then additionally the drive providing themutual rotation of two modules. [3]

2. Throwable robots

THROWABLE TACTICAL ROBOT – DESCRIPTION OF

CONSTRUCTION AND PERFORMED TESTS

Rafał Czupryniak, Maciej Trojnacki

Received 27 ; accepted 30th July 2010 August 2010th


Fig. 1. Throwable Tethrahedral Mobile Robot an its use conception [3].

Articles26

There are several throwable robots sold on the mar-ket, among others SpyBowl 360, Eye Ball, Recon Scoutand EyeDrive. Almost each of those devices has a diffe-rent construction idea of making teleobservation andtracing possible. [1], [5]

SpyBowl (Fig. 2a) is a device thrown or rolled towardsthe target. The device is made as aluminium body coveredwith rubber coating in form of a ball with 115 mm in dia-meter. Such a construction allows for the transport of lar-ge, repeated loads. It is equipped with four cameras allo-wing for the acquisition of static images (Fig. 2b) andwith microphones transmitting the sound. The device canrotate about its vertical axis with speed of 0.22 rad/s,which allows us to watch all environment in dynamic way.Additionally the image can be seen from each cameraindependently. The range of the radio transmission variesbetween 20-30 meters inside building and 100-300 moutside. Entire device weighs 1 kg and can be thrown atthe distance of 30 meters or thrown up to the height of 6meters. Operating time on a battery is 45 min. The mainapplication place of the SpyBowl device are closed roomsand buildings in the action zone of military and policespecial forces. [1], [5]

A similar device, regarding design, is Eye Ball R1 (Fig.3). It is designed for throwing at the distance of 50meters, rolling or dropping. It provides an audio and vi-deo transmissions in real time. The device is used intactic operations, where special forces take the advan-tage of newest information about situation in given

(a)

(b)

Fig. 2. Throwable robot SpyBowl (a) and the view of onethe robot`s cameras (b) [5].

place, straight before entering upon an intervention. Thedevice has one camera providing a good quality picture to23 meters. In order to collect complete informationabout the environment the device rotates about its ownaxis with the speed of 4 turns/min. Thanks to an extrasoftware it is possible to acquire a panoramic view. Besi-des, the device has near infrared illuminators of the ran-ge of 8 meters and thanks to them the camera is able tosee in the darkness. The microphone has the range of5 meters. Operating time on battery is 2 hours, in stand-by mode - 24 hours. Radio and video transmission takesplace at a distance up to 125 meters depending on theenvironment. [1], [4], [7]

The third interesting device for teleobservation andtracing is the Recon Scout robot. It is a mobile two-whe-eled robot with titanic body and wheels from the uretha-ne plastic. Such a construction allows throwing the robotat the distance up to 31.5 meters and dropping from theheight of 9.1 meter. Moving forward is enabled by the so-called tail, which is the robot's support. Robot's parame-ters are following: width 187 mm, wheels diameter 76mm, speed 1,1 km/h, range inside the building to 30 me-ters, outside 76 meters, working time 1 hour. The robot isequipped with black&white camera with sensitivity of0,0003 lux. Due to small size it succeeded to obtain a to-tal weight of the device - 0.544 kg. [1],[6]

The last presented robot is EyeDrive (Fig. 4). This isa four-wheeled robot produced in Israel (with the possi-bility to use a caterpillar track) operated by a single man.The robot can be thrown up to 3 meters high. The systemof cameras allows for obtaining a panoramic view withimage definition of 2500x570 pixels. The microphonetransmits sound from the distance of 10 m. The robot's

Fig. 3. Throwable robot Eye Boll [7].

Fig. 4. Robot EyeDrive [7].


Articles 27

Discarding height (limiting) 9 mRange inside building 30 mRange in open space 100 mStandard equipment Camera,

microphone

Robot's body (Fig. 6a) is a specially formed cylinderwhich is an assembling base for all construction elementsboth outside and inside. Inside the body there are maderibs for double purpose. They are the elements whichstrengthen the shell of the body against deformation andfix the components of the robot. Thanks to the internalribs it is possible to easily mount electronic boards on oneside (Fig. 6b) and the battery on the other (Fig.6c). In thecentral part of the body the camera and microphone arefixed. A special micro junction is used for connecting therobot to the additional operational load, the so-calledrucksack, its detection and releasing.

The engines are seated in properly formed sleevesattached to the body. Wheel rims are fixed to external ex-treme parts of the body by means of the bearings. Here,

Fig.5. The first conception of TRM's construction (section).

(a)

(b)

(c)

Fig. 6. Construction design of TTR: additional device „ruck-sack” (a), position of electronic plates (b) and battery (c).

3.2. Robot construction

range inside the building is 70 meters and outside to 300meters. Operating time on battery is 3 hours and instand-by mode - 24 hours. The robot`s weight is 2.3 kg,there is a possibility to carry additional loads (sensors,explosives, etc.) weighing up to 3 kg. [1], [7]

Summing up the review of throwable mobile robots wecan presume that the future of robotics and consequentlyof mobile robots looks promising. According to the deve-lopment of technology and electronics we can expecta wider use of remotely controlled and autonomous de-vices. They assure safe accomplishment of the task with-out endangering people`s life. The only eventual loss canbe damaged technical unit. [1]

3. Throwable tactical robot

Throwable tactical robot (TTR) has been designed foractive teleobservation in military, police and rescue ap-plications. It is a solution for threats which brings re-connaissance done by special forces before starting theaction.

TTR is a device, which can be placed at the target areafrom a considerable distance and then survey it whilebeing teleoperated. The camera and microphone placedinside the robot and its mobile abilities result in it beinga perfect reconnaissance device limiting significantly therisk of health or life loss of a group members performingactions in the dangerous area. In assumption the TTR canbe equipped with additional external device, the so-calledrucksack, which enables to carry specialised charges:flashbangs, deafening and explosives. Additional equip-ment enables TTR use for explosive charges neutralizationby pyrotechnic troops or making disorganisation andpanic in the aggressors group.

The construction of the robot has been developed asa part of the developement project for which Table 1 con-tains the assumption data. The design work over the robothas been partially supported by analisys done with theusage of MD Adams and Ansys software.

Two different models of the device have been evolved.According to the first solution (Fig. 5), the robot was sup-posed to have a trunk, being at the same time the runninggear.

The first idea has been abandoned, because of the for-seen technological and technical difficulties with moun-ting and exploatation.

The second conception of the robot's constructiondeveloped in the project is desribed in point 3.2. It ischaracterized by greater compactness and funcionalitythanks to the ability to join additional load to the trunk.It was not possible in the previous version of the device.

Robot's weight in standard version 1 - 1.5 kgWeight of additional load 0.1 kgWeight of control panel 6-8 kgMaximum speed 3 km/hThrowing range 20 m

3.1. Device conception

Parameter Desired value

Table. 1. The desired parameters of the throwable tacticalrobot.


Articles28

the kind of the bearing is very important because of itswear as a result of an impact, friction and price. Drivetransmission is a result of meshing of the rack embeddedin engine axis and inside gear embedded in the rim. As anoverload coupling for the protection of gears and theengine there are applied micro rubber blocks placed incut-outs of the ring with internal teeth. They enablegradual angular shift against the rim.

The made prototypes of the device and control panelare shown in Fig. 7 and the most important parameters ofthe device are presented in Table 2.

Robot's weight in standard version 1.3 kgWeight of additional load 0.16 kgWeight of control panel 7 kgRobot size (width/ height/length) 205/100/210 mm

(with tail)Control panel size 360x340x194 mmMaximum speed 3.3 km/hMaximum ramp angle 25 degThrowing range 15 - 20 mDiscarding height (limiting) 7 m (9 m)Range inside building 30 - 110 m

(a)

(b)

Fig. 7. Prototype TTR (a) and control panel (b).

Table. 2. The most important parameters of the throwabletactical robot.

Parameter Value

Range in open space 120 - 150 mStandard equipment camera,

microphoneRadio transmission telemetry, visionOperating time 1 hControl panel operating time 4 hMaximal number of controlled devices 3

The range of robot mentioned in Table 2 directly de-pends on environmental condition of the radio waves pro-pagation.

Shock absorption on contact with the ground afterthrowing is assured by appropriately cut T-shape tread onthe wheel. The additional sideways shock absorption isassured by rubber straps.

High maximal robot's speed is 3.3 km/h and enables toperform inside reconnaissance efficiently and time spa-ring. Higher speed value would be a significant obstruc-tion for the operator so the reached result seems to beoptimal.

The device is switched on in non-standard way, thatis, by turning the wheel and switched off remotely fromthe console or after longer inactivity time. Such a switch-ing on should make it service easier by the operator wear-ing gloves. In order to save energy the device automa-tically limits power consumption by unused components.The robot is provided with an internal connection whichhelps to communicate with other robots and initiateexplosives.

The electronic part of the device is divided into follo-wing functional blocks: supply module, micro controllerwith peripheries managing the model's functions, enginedrive programmer, vision transmitter, telemetry receiver,interface scheduling CAN BUS.

Cameras with good optical characteristic, working alsoin infrared band are applied in the device. The advantageof such a solution is operating the robot in insufficientlightning and in the darkness what results with better pic-ture quality and makes the work more comfortable.

Control unit has form of an unfolded box of 330x234x170 mm and weight 7 kg. A special construction assureshigh stiffness, shock and bending resistance. The box hasa special seal which effectively protects it from sand anddust and assures complete water resistance and water-proofness up to 10 meters. Material, which the box is ma-de from, is very durable in temperatures from -33°C to+90°C and resistant to oils, lubricants and other aggres-sive substances.

There are positioned antenna, monitor and two loud-speakers in the box lid. Application of directional antennaenables to acquire high power gain and directivity of radiobeam. Additionally small size of the antenna enabled tobuild it in completely in the box lid what protects it frommechanical damage and increases functionality of thecontrol panel. The operator observes the picture from thedevice camera on the monitor and through loud speakers,that are built in on monitor sides, can hear sound from themicrophone installed on the device. The use of the moni-tor with a TFT matrix allows for obtaining a picture of bet-ter quality and brightness than the usual LCD matrix. The

�

�

3.3. Control panel


Articles 29

TFT matrix assures lower power consumption as well,which is essential in case of battery use. The control deskis positioned at the bottom of the box. It is equipped withone joystick and push-buttons responsible for operatingdifferent device functions. Behind the control desk (syn-optics) are placed all the electronics controlling thecontrol panel and the exchangeable battery package.

The control panel is divided into modules of synoptics,mainboard and transmission. It should largely facilitateservicing and operating the control panel. The control pa-nel is supplied by exchangeable eight-cell lithium-poly-mer battery package. It is characterized by low self-dis-charging so it can be stored for a longer time withoutrecharging. Additionally there is no memory-effect in itscase. The exchangeable battery pack is integrated withthe side grip of the operating panel what enables fastbattery change. In the front part of the control panel areaudio-video junctions enabling recording and reproduc-tion of registered actions.

Three devices can be controlled from one control panelindependently. It increases the functionality of the setand reduces the risk of the device uselessness in case ofradio contact loss between the device and control panel ordevice damage. Possibility of switching among three de-vices allows also for having three independent observa-tion points.

Special electronic systems built on base of single-sys-tem processors are designed for the control panel needs.Those systems are optimized due to EMC interferences,thermal overload or errors of transmission and adequatestandard signal.

The control panel is designed as a general-purposeone. On the PCB panel of the control panel are placed2 joysticks and 28 push-buttons, where 16 are illumina-ted. Additionally there are 3 diode lines. All elements canbe used in an arbitrary way according to the needs.

For the robot prototype was done number of tests invarious conditions.

The first test consisted in performing a series of20 throws of the device at a distance of 15-20 meters ina straight line on concrete base. Pending those throwsthere was no construction damage, it means, the devicewas still fully operative and ready to follow commandsfrom the control panel.

The second test consisted in throwing the device intorooms through the open window (Fig. 8a). It enabled towork out the throwing technique, its evaluation and pre-cision. In that test there were no damages, neither me-chanical nor control system.

The third test consisted in series of dropping from theheight of the 2 floor, that is, from about 9 meters (Fig.8b). The fall from such a height enables to acquire speedof 48 km/h. It follows from the tests that this case is themost difficult and demanding. In the worst case the fullload is received and transferred by one wheel and bearingto the body construction. In result of the tests there werechanged the rubber strap on the rim dispersing andabsorbing the fall as well as the ball bearings to crosswiseroller bearings.

3.4. Tests of the robot and the control panel

nd

(a)

(b)

Fig. 8. Throwing tests into a room (a) and dropping fromthe second floor (b).

The aim of next tests was to determine limiting rangevalues of telemetry and vision transmitter. One of themost essential questions was to study possibilities tomove inside buildings. It is well-known that construc-tions of most buildings are made of reinforced concrete.Such a building construction causes both strong suppres-sion and dispersion of electromagnetic waves. The mostfrequent result is the loss of radio communication whichmakes further control of the device impossible. In mostcases the vision data are lost firstly, which prevents theoperator from visual control over drive direction. The nextis loss of telemetry range. After losing the image there ispossible to transmit the sound. In some cases only lis-tening is sufficient, however it limits evidently possibili-ties to acquire valuable information about dangeroussituation.

The telemetry and vision range was satisfactory up to100-110 meters. Both transmissions had continuous andnon-disrupted character enabling efficient task perfor-mance. The result is impressive regarding small size of thedevice, considerable proximity of ground introducingnoise and just coincidental shading of a direct view bet-ween the panel and the device. Tests in open area demon-strated that the transmission range is not shorter than110-150 meters. It offers great opportunities for thedevice application not only to inspect car`s chassis but allkind of reconnaissance around buildings or other deviceof special purpose. The reconnaissance zone is largeenough to recommend usage of this device by military py-rotechnic troops, police and rescue units. Application ofadditional load allows for taking a counter-load and itsdetonation in justified cases.


Articles30


During further tests there was done a drive down thestairs to the basement in the building with limited illu-mination and space reconnaissance with use of the came-ra working in infrared mode. All stairsteps were surmoun-ted autonomously without operator's intervention. Bothorientation in the corridor and reconnaissance were per-formed at moderate light which allowed for testing thequality of the picture sent by the device and determiningthe device usability in such conditions.

At moderate light it was possible to observe the base-ment and identify detailed furnishings. The robot's came-ra was not equipped with illuminators so for observationof places like a basement an infrared radiation must beprovided. Nowadays works on attaching an illuminator areconducted what can enable to do a reconnaissance intotal darkness. There will be tested diode illuminators ofvisible radiation and infrared radiation.

The next tests consisted in driving down the stairs(Fig. 9a). They were the simplest due to easy access to thestaircase, its large space and good illumination. Duringthe decent the picture observation is not possible due tofast frame changing and variation of direction of cameraview. The descent itself has rather random character. Itdoes not cause any danger neither for the device nor theenvironment. The worst case that can happen is rotationaround the longitudinal axis and driving the stairs side-ways. In this case the device gets pretty large rotationspeed and large driving down speed and the operator isnot able to control the drive till the moment when thedevice stops.

In the next tests the throw range of the device wasexamined (Fig. 9b). Because the construction weight is1 kg the throw range depends on a large measure on thethrower. The obtained results of 15-20 meters dependsadditionally on the way of falling, that is, if the devicestarts to overturn at touchdown.

From obtained results we can conclude that the thro-wer should have no problems by delivering the deviceboth to a long distance and i.e. roof of a one-floorbuilding.

(a)

(b)

Fig. 9. Tests of driving downstairs (a) and distance throwing(b).

There were performed tests in the arrival hall at OkęcieAirport as well (Fig. 10a) in co-operation with the BorderGuard. The hall is characteristic due to its construction,which is reinforced strongly and has a lot of steel con-struction elements. Such conditions cause a special pro-blem for radio modems due to strong damping of radiosignal and a large number of signal rebounds from thoseconstructions. Test drives were performed in time ofnormal flight service in order to show real operational usecloser and to obtain additional factors that can influencethe communication quality with the device.

Performed tests allowed to cover the distance of 80meters on the way between screening plan of terminalsT1 and T2. Additionally tests drives were done betweenseparate transporters due to maximize quantity and levelof interferences both from the transporter constructionand its work. The reconnaissance proceeded without sig-nificant problems although the device was screened direc-tly through protective elements of the luggage trans-porter.

Special tests were performed on the board of Boeing737 of Polish Airlines LOT (Fig. 10b). Their task was topresent possibilities to do reconnaissance in a very diffi-cult place like passenger cabin. The problem results fromsmall device size and large number of elements genera-ting disturbances. Support elements of the seats are a ve-ry dense obstacle for propagation of waves and generatea large number of reflections diminishing primary radiosignal. In such special circumstances the radio communi-cation and possibility to access each corner of the fuse-lage of the aeroplane construction was tested. The tests

(a)

(b)

Fig. 10. Device tests in the arrival hall of Okęcie Airport (a)and on the board of Boeing 737 (b).

VOLUME 4, N° 4 2010

Articles 31


of the device were performed in this Boeing model due toits significant popularity and in connection with greatprobability of necessity to reconnaissance just this con-struction.

During tests the reliability of load release mechanismwas tested (Fig. 11), both on the mechanism and the soft-ware. The use of explosive charges should, depending onthe character of the special forces actions, introduce cha-os and panic amongst aggressors and lead to neutraliza-tion of dangerous and dubious packages on spot.

It enables the large spectrum of using the device inpotential events and scenarios.

Additional load can carry different materials, inclu-ding explosives, deafening and blinding charges. The cha-racter of applied material depends in every case on thekind of activity and usage context. You should take intoconsideration that in case of using explosive material thedevice will be destroyed without chance to repair it. Thecost that it will entail is not of great importance due tothe fact of using it in special, rescue or other actions.

Films presenting selected versions of the robot are atthe link [8].

In this paper the construction and working mode ofthe throwable tactical robot and its control panel is pre-sented.

Test results testify that the robot is resistant to thedownfall caused by throwing down, descent or droppingfrom the second floor. The shape and mass of the robotenables to throw it at the distance of 15-20 meters or tothe roof of one-floor building. Application of the cameraworking in the infrared mode enables a reconnaissanceby meanlight. The robot copes very well in surveying noteasily accessible spaces and places where the radio com-munication is difficult. The communication range en-ables teleoperating the device both in open area and inrooms adequately to 110 and 150 meters. The transmis-sion ranges obtained in these cases are highly satisfyingconsidering the size of the device.

Such attributes of the robot predispose it to activeteleobservation in military, police and rescue use. Addi-tional equipment allows to use TTR to neutralization ofexplosive charges by special forces. The robot enables tolimit the risk of health or life loss or group membersperforming actions in dangerous areas.

Fig. 11. Reliability tests of the mechanism releasing explo-sive charge.

4. Summary

ACKNOWLEDGMENTS

AUTHORSRafał Czupryniak, Maciej Trojnacki*

References

The presented work has been financed from the research projectsponsored by the Ministry of Science and Higher Education cal-led “Ultradurable robotized devices to active teleobservation,usable in military, police and rescue purposes”(R00-00058/3).

[1] R. Czupryniak, P. Szynkarczyk, Trojnacki M., “Tenden-cies in the development of mobile ground robots (2)New trends in mobile robotics”, , no. 7-8, 2008,pp. 10-13. (in Polish).

[2] P. Szynkarczyk, R. Czupryniak, “Mobile robots and secu-rity”, , no. 2/2008, appending on CD, pp. 441-450.

[3] K. Tadakuma, R. Tadakuma, K. Nagatani, K. Yoshida, M.Aigo, M. Shimojo, K. Iagnemma, “Throwable Tetrahed-ral Robot with Transformation Capability”. In:

, 11 -15 October, 2009 St. Louis, USA,pp. 2801-2808.

[4] E. Ackerman, Throwable EyeBall R1 Surveillance Robot,20 of August 2009 available at:http://www.botjunkie.com.

[5] Defense Update Online Defense Magazine:http://www.defense-update.com.

[6] Official web page of ReconRobotics Inc.:http://www.recon-scout.com.

[7] Official web page of ODF Optronics Ltd.:http://www.odfopt.com.

[8] Video clips presenting some PIAP's mobile robots inaction : http://www.youtube.com/user/osmpiap.

- IndustrialResearch Institute for Automation & Measurements,Al. Jerozolimskie 202, PL-02-486 Warsaw, Poland.E-mail: [email protected].* Corresponding author

PAR

PAR

2009IEEE/RSJ International Conference on Intelligent Robotsand Systems th th

VOLUME 4, N° 4 2010

Articles32


SPECIAL ISSUE

Editorial to theSpecial Issue Section on

Hybrid Intelligent Systemsfor Control and Automation

Part I

Guest Editors:

Oscar Castillo and Patricia Melin


Editorial to the Special Issue Section on

“Hybrid Intelligent Systems for Control and Automation - Part I”

The special issue on hybrid intelligent systems for control and automation comprises four contributions,which are selected and extended versions of papers previously presented at the International Seminar onComputational Intelligence held at Tijuana, Mexico on January of 2010. The papers describe differentcontributions to the area of hybrid intelligent systems with application on control and automation. In thepapers, an optimal combination of intelligent techniques is applied to solve in an efficient and accuratemanner a problem in a particular area of application.

In the first paper, by Ieroham Baruch and Carlos-Roman Mariaca-Gaspar, Recurrent Neural Identificationand Control of a Continuous Bioprocess via First and Second Order Learning is presented. This paper applieda new Kalman Filter Recurrent Neural Network (KFRNN) topology and a recursive Levenberg-Marquardt (L-M)learning algorithm capable to estimate parameters and states of highly nonlinear unknown plant in noisyenvironment. The proposed KFRNN identifier, learned by the Backpropagation and L-M learning algorithm,was incorporated in a direct and indirect adaptive neural control schemes. The proposed control schemeswere applied for real-time recurrent neural identification and control of a continuous stirred tank bioreactormodel, where fast convergence, noise filtering and low mean squared error of reference tracking wereachieved.

In the second paper, by Yazmin Maldonado , a Novel Method for Genetic Optimization of Member-ship functions of Fuzzy Logic for Speed Control of a Direct Current Motor for Hardware Applications in FPGAsis presented. This paper proposes a novel method for genetic optimization of triangular and trapezoidalmembership functions of fuzzy systems, for hardware applications such as the FPGA (Field ProgrammableGate Array). This method consists in taking only certain points of the membership functions, with the purpose of giving more efficiency to the algorithm. The genetic algorithm was tested in a fuzzy controller toregulate engine speed of a direct current (DC) motor, using the Xilinx System Generator (XSG) toolbox ofMatlab, which simulate VHDL (Very High Description Language) code.

In the third paper, by Héctor Joaquín Fraire Huacuja , a method for Improving the Intensificationand Diversification Balance of the Tabu Solution for the Robust Capacitated International Sourcing Problemis presented. This paper addresses the robust capacitated international sourcing problem (RoCIS), whichconsists of selecting a subset of suppliers with finite capacity, from an available set of potential suppliersinternationally located.

In the fourth paper, by Abraham Meléndez , the Optimization of a Reactive Controller for a MobileRobot using Evolutionary Algorithms and Fuzzy Logic is presented. This paper describes an evolutionaryalgorithm used for the optimization of a reactive controller applied to a particular mobile robot. The algorithm optimizes the Fuzzy Inference System and the position and number of the sensors on the robot, whiletrying to use the minimum amount of power possible.

In conclusion, this special issue represents a contribution to the state of the art in the area of hybridintelligent systems with application on control and automation.

Oscar Castillo and Patricia MelinTijuana Institute of Technology, Tijuana, [email protected], [email protected]

et al.

et al.

et al.

-

-

Guest Editors:

Editorial

Oscar Castillo*, Patricia Melin

35Editorial

VOLUME 4, N° 4 2010

Abstract:

1. Introduction

This paper applies a new Kalman Filter Recurrent NeuralNetwork (KFRNN) topology and a recursive Levenberg-Marquardt (L-M) learning algorithm capable to estimate parameters and states of highly nonlinear unknown plant innoisy environment. The proposed KFRNN identifier, learnedby the Backpropagation and L-M learning algorithm, wasincorporated in a direct and indirect adaptive neural control schemes. The proposed control schemes were appliedfor real-time recurrent neural identification and controlof a continuous stirred tank bioreactor model, where fastconvergence, noise filtering and low mean squared errorof reference tracking were achieved.

--

-

backpropagation learning, continuous stirredtank bioreactor, direct adaptive neural control, indirectadaptive sliding mode control, Kalman filter recurrentneural network identifier, Levenberg-Marquardt learning.

Keywords:

The universal approximation abilities of the artificialneural networks to approximate complex non-linear rela-tionships without prior knowledge of the model struc-ture, makes them a very attractive alternative to the clas-sical modeling and control techniques [1], [2], [3]. Thisproperty has been proved by the universal approximationtheorem [3]. Among several possible network architec-tures the ones most widely used are the Feedforward(FFNN) and the Recurrent Neural Networks (RNN). Ina feedforward neural network the signals are transmittedonly in one direction, starting from the input layer, sub-sequently through the hidden layers to the output layer,which requires applying a tap delayed global feedbacksand a tap delayed inputs to achieve a nonlinear autore-gressive moving average neural dynamic plant model.A recurrent neural network has local feedback connec-tions to some of the previous layers. Such a structure issuitable alternative to the first one when the task is tomodel dynamic systems, and the universal approximationtheorem has been proved for the recurrent neural net-works too. The preferences given to recurrent neural net-work identification with respect to the classical methodsof process identification are clearly demonstrated in thesolution of the “bias-variance dilemma” [3]. Further-more, the derivation of an analytical plant model, theparameterization of that model and the Least Squaresolution for the unknown parameters have the followingdisadvantages: (a) the analytical model did not includeall factors having influence to the process behavior; (b)the analytical model is derived taking into account some

simplifying suppositions which not ever match; (c) theanalytical model did not described all plant nonline-arities, time lags and time delays belonging to the pro-cess in hand; (d) the analytical model did not include allprocess and measurement noises which are sensor andactuator dependent. In (Sage, [4]) the method of inva-riant imbedding has been described. This method seemedto be a universal tool for simultaneous state and parame-ter estimation of nonlinear plants but it suffer for thesame drawbacks because a complete nonlinear plant mo-del description is needed. Furthermore, the managing ofnoisy input/output plant data is required to augment thefiltering capabilities of the identification RNNs, [5].Driven by these limitations, a new Kalman Filter Recur-rent Neural Network (KFRNN) topology and the recursiveBackpropagation (BP) learning algorithm in vector-ma-trix form has been derived [6] and its convergence hasbeen studied [6], [7]. But the recursive BP algorithm,applied for KFRNN learning, is a gradient descent firstorder learning algorithm which does not allow toaugment the precision and accelerate the learning [5],[7]. Therefore, the aim of this paper was to use a secondorder learning algorithm for the KFRNN, as the Leven-berg-Marquardt (L-M) algorithm is, [8]. The KFRNN withL-M learning was applied for Continuous Stirred TankReactor (CSTR) model identification [9], [10]. The appli-cation of KFRNNs together with the recursive L-M couldprevent all the problems caused by the use of the FFNN,thus improving the learning and the precision of theplant state and parameter estimation in presence ofnoise. Here, the parameters and states, obtained fromthe KFRNN identifier will be used in order to designa Direct and Indirect Adaptive Neural Control (DANC andIANC) of CSTR bioprocess plant model.

(1)

2. Kalman Filter RNNThis section is dedicated to the KFRNN topology, the

recursive Backpropagation and the recursive Levenberg-Marquardt algorithms for the KFRNN learning. The KFRNNis applied as a state and parameter estimator of nonlinearplants.

Let us consider the linearized plant model (1), (2),represented in a state-space form:

(2)

Where: means mathematical expectation; the pro-

2.1. Topology of the KFRNN

X k+ = A k X + B U +

Y = C (k) X (k) + (k)

E

d.( 1) ( )

[.]

�

�

d d d

d d d

( ) ( ) ( ) ( )

( )

k k k k

k

1

2

RECURRENT NEURAL IDENTIFICATION AND CONTROL OFA CONTINUOUS BIOPROCESS VIA FIRST AND SECOND ORDER LEARNING

Ieroham Baruch, Carlos-Roman Mariaca-Gaspar


Articles 37

cess and measurement noises , are white,with , and the initial state inde-pendent and zero mean for all , , with known variances

, whereif , and otherwise. The optimal Kalman filter

theory is completely described in [4], and we would notrepeat it here. For us the Kalman Filter (KF) is a full rankoptimal state estimator capable to estimate the systemstates, to filter the process and measurement noises, taking in hand all plant information available like: input/output plant data, all parameters of the plant model (1),(2), and the given up noise and initial state statistics(mean and variance). The basic Kalman filter equationsfor the estimated state and output variables are given by:

(3)

(4)

(5)

Where: is the estimated state vector withdimension is a closed-loop KF statematrix; is the estimated plant output vectorvariable with dimension is the optimal Kalmanfilter gain matrix with dimension . This gainmatrix is computed applying the optimal Kalman filteringmethodology given in [4]. So, the KF performed noisefiltration by means of an optimal closed-loop feedbackwhich has the drawback that the feedback amplified thenoise components of the error, especially when thefeedback gain is high. The second drawback is that the KFdesign needs complete plant parameter and noiseinformation, which means that if the plant data are incomplete the process noise level is augmented. To overcome this we need to take special measures like to augment the filtering capabilities of the KF. The third drawback is that the KF could not estimate parameters andstates in the same time processing noisy measurementswith unknown noise statistics, and it will be our task. Toresolve this task we need to derive the topology and theBP learning algorithm of a new recurrent KF-like neuralnetwork subject of learning and capable to estimate parameters and states in the same time. First of all we couldrewrite the equation (3) defining a new extended inputvector, containing all available input/output information issued by the plant, and second we could modifythe output equation (5), so to convert it to an outputnoise filter. After that we obtain:

� �

�

� � �

� � � � �

�

(.) (.)

[ (k)] = , [ ( ) ( )] = Q( )( - ), E[ ( ) ( )] = ( ) ( - ) ( - ) =1 = 0

( +1) = A ( ) X ( ) + K ( ) Y ( ) + B ( ) ( )

( ) = ( ) - ( ) ( )

( ) = ( ) ( )

( ); ( ) ( x )

( ); ( )

( x )

1 2

2 0

0 1 1

2 2

1 Xk s

E X P E k k kk k k R k k k

k

X k k U k

A A K C

Y C X

Xe kN A k N N

Y kL K k

N L

( ) ( ) ( )

( )

k s k

X k

k k k k

k k k k

k k k

�

� �

d

d d

d. e e e d d

d d d d

e d d

e e e e

e

e

e

T

T

T

-

----

-

--

X k+ = A k X - K Y + B U

B = B ; K ; U = U ; Y

Z = C X

Y = A Y + Z

X k k

B = B ; B ; UT = U ; U

A A A

Z k G X k

C C C Z Z

V = CZ

V k+ = V + A V

A

Y F V

X, Y, UN, L, M

Z LZ U N

MZ U V

LT A

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B C N LF

G

U B

D

( 1) ( )

[ ] [ ]

( +1) = A X + BU( ) - DY

[ ] [ ]

= block-diag ( ), | | < 1

( ) = [ ( )]

= [ ; ]; Z = [ ; ]

( 1)

= block-diag ( ), | | < 1

= [ ]

( +1)( +1)

( x1)( x1)

= -1, = -1( x1)

1, 2( x ) ( x )

[ ( +1)] [ ( +1)]( x1) ( x1)

[.][.]

(6)

(7)

(8)

(9)

The obtained new KF RNN topology is given in Fig. 1.The first layer of the KFRNN represented the plant

model (equations (10)-(13)) and the second layer -represented the output noise filtering model (equations(14)-(18)). The KF RNN topology is described by thefollowing equations:

(10)

(11)

(12

(13)

(14)

(15)

(16)

(17)

(18)

Where: are vectors of state, output, and augmented input with dimensions , respectively,

is an dimensional input of the feedforwardout put layer, where and are the output and

input of the hidden layer; the constant scalarthreshold entries are , respectively; isa pre-synaptic activity of the output layer; thesuper-index means vector transpose; are

and block-diagonal weight matrices;and are and - augmentedweight matrices; and are andthreshold weights of the hidden and output layers; ,

are vector-valued tanh(.) or sigmoid(.) -activationfunctions with corresponding dimensions. Here the inputvector and the input matrix of the KF RNN are augmented so to fulfill the specifications (7) and the matrix

corresponded to the feedback gain matrix of the KF.

e. d e e e e

d e e d

d e

e e

i

i i

d

( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

( 1) ( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

k k k k k

k k k

k+ k k

k k

k k

k k

A A

k k

A

2

2

2

1

1 0 1 2

1 1,

1

1 0 1 2

1

1 2

1 2, 2,

1 1

2 2

0 0

T

T

)

-

--

-

1,i


Articles38

VOLUME 4, N° 4 2010

Fig. 1. Block-diagram of the KFRNN topology.

matrices , are denoted by ,, respectively, where (24), (30) represented their

learning as an element-by-element vector products;are error vectors (see Fig. 2), predicted by the

adjoint KF RNN model. So, the KF RNN is capable to issueparameter and state estimations for control purposes,thanks to the optimization capabilities of the BP learningalgorithm, applying the “correction for error” delta ruleof learning (see Haykin, [3]). The stability of the KF RNNmodel is assured by the activation functions bo-unds and by the local stability weight bound conditionsgiven by (12), (17). The stability of the KF RNN move-ment around the optimal weight point has been provedby one theorem and the rate of convergence lemma, (seethe Ph.D. thesis of Mariaca [7]). It is stated below.

Theorem of stability of the BP KF RNN used as a plantidentifier [7]: Let the KF RNN topology is given by equations (10)-(18) (see Fig.1) and the nonlinear plant model, is as follows:

(31)

(32)

Where: are output, state and inputvariables with dimensions , respectively; ,

are vector valued nonlinear functions with respec-tive dimensions.

Under the assumption of KF RNN identifiability made,the application of the BP learning algorithm for

, in general vector-matrix form, described byequation (19)-(30), and the learning rates(here they are considered as time-dependent and normalized with respect to the error) are derived using thefollowing Lyapunov function:

(33)

Where: and are given by:

Where:

Vec k

E,E , E , E ,

X = G X , U

Y = F X

Y UL, N , M G

F

C, A ,A , B, D

k

L(k) = L + L

(A ( ))

[-1, 1]

[ ]

[ ]

{ (.), (.), (.)}(.)

(.)

( ), ( )

A A Veck

k k k

k k

X

k

k k

L k L k

1 2 1

2

1 2 3

1

2

1 2

1 2

(A ( ))

( +1) ( ) ( )

( ) ( )

( ) ( )

( ) ( )

--

-

d. d

d d

d d

d

� �

The dimension of the state vector of the KF RNN is chosenusing the simple rule which is: . From Fig.1 wecould see that here we have a two layer Jordan canonicaltopology with a global feedback which filtered the process noise better then a two layer feedforward topologycontaining input and output tap delays representinga successive noise sensitive NARMA model, [6].

So the KF RNN topology corresponded functionally tothe KF definition (6)-(9) and ought to be learnt applyingthe BP learning algorithm derived using the adjoint KFRNN (see Fig. 2) based on KF RNN topology applying thediagrammatic method, [11].

The BP learning algorithm, expressed in vector-matrixform is as follows:

(19)

(20)

(22)

(23)

(24)

(26)

(27)

(28)

(30)

Where: , are derivatives of the tanh acti-vation functions; is a general weight, denoting eachweight matrix in the KF RNN model, tobe updated; , is the weight correctionof ; is an L-dimensional output of the approximatedplant taken as a reference for KF RNN learning; , arelearning rate parameters; is an weight correction of

; is an weight correction of ; is an weightcorrection of , is the weight correction of ,is the weight correction of ; the diagonals of the

N=L+M

W k = W k + W + W |W | < W

E = Y - Y ; E = F' Y E

F' Y = -Y

C = E Z

A = E V

Vec( A ) = E X

E = G' Z E ; E = CT E

G' Z = -Z

B = E U

D(k) = E (k) Y

A k = E X

Vec(A ) = E X

F G

C B DW C, B, D

W Y

CC B B D

DA

-

(21)

(25)

(29)

2.2. BP Learning of the KFRNN

( +1) ( ) ;

[ ]

[ ] [1

[ ]

[ ] [1 ]

( )

'[.] '[.] (.)

( , , , , )( )

ij( ) ( 1)

( ) ( ) ( ) ( ) ( ) ( )

( ) ( )]

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

( ) ( )

( ) ( ) ( )

( )

( ) ( )

( ) ( ) ( )

, ,

k k

k k k k k k

k k

k k k

k k k

k k k

k k k k k k

k k

k k k

k

k k

k k k

WA AA A

A A A

�

�

�

�

0

1

1

2 1

2 1

3 2 2 1

3

3

1 3

1 3

1 2

1 2

1 1 2

2

d

d

2

2

T

T

T

T

T

� �


Articles 39

VOLUME 4, N° 4 2010

Fig. 2. Block-diagram of the adjoint KFRNN topology.

T

T

T

T

T

L k W W W W2 1( ) 1( ) 2( ) 2( )( ) = tr ( ) + tr ( ) +A k A k A k A k

W A A W A AA k k A k k1( ) 1( ) 1 2( ) 2( ) 2= =� � � �

W B B W C CB k k C k k( ) ( ) ( ) ( )= =� � � �

W D DD k k( ) ( )= �

tr ( ) + tr ( ) +W W W WB k B k C k C k( ) ( ) ( ) ( )

tr ( )W WD k D k( ) ( )

�

�

�

�

�

*

*

*

*

*

are vectors of the weight estimation error andand denoted the

ideal neural weight and the estimated neural weight atthe k-th step, respectively, for each case.Then the identification error is bounded, i.e.:

(34)

(35)

Where the condition for is fulfilled whenthe maximum learning rate is chosen in the limits, givenbelow:

For fulfillment we have the condition:

Note that changes adaptively during the learning process of the network, where:

Here all: the unmodeled dynamics, the approximationerrors and the perturbations, are represented by the d-term, and the complete proof of that theorem and theconvergence lemma for (36) are given in the Appendix Aand can be seen also with more details in [7].

The general recursive L-M algorithm of learning, [5],[7], [8] is given by the following equations:

Where: is a general weight matrix andunder modification; is the covariance matrix of the

estimated weights updated; is an -dimensionalgradient vector; is the KFRNN output vector whichdepends of the updated weights and the input; is anerror vector; is the plant output vector, which is in factthe target vector. Using the same KFRNN adjoint blockdiagram (see Fig.2), it was possible to obtain the valuesof the gradients for each updated weight, propa-gating the value through it. Following the blockdiagram of Fig. 2, equation (37) was applied for each ele-ment of the weight matrices in orderto be updated. The corresponding gradient components(40) are obtained as follows:

() ( )

( 1) ( 1) ( 1)

( 1) ( 1)

+1) < max e +1)max e ) +1)

max

max({ }

( 1) ( ) ( ) [ ( )] [ ( )]

[ ( )] [ ( ), ( )]

[ ( )] ( ) [ ( ), ( )]

[ ( )] [ , ( )]

[.]

, , ,

[ ( )] ( ) ( )

A , A , B ,C , D A , A , B , C , D

k+ k+ k+

k+ k+

+

=

W k+ = W k + P k Y W k E W k

Y W k = g W k U k

E W k = {Y k g W k U k }

DY W k = g W U k

A A

DY

A A B C

DY C k = D k Z k

1 2

1( ) 2( ) ( ) ( ) ( )

1 2

1 2

1,

k k k k k

i

p

ij i j

L = + <

L = L L

W B CD P

DY NwY

EY

D k I

D

0

)

+1) < 0

+1) < 0

( , , , ,)

[.]

( ) =

( , )

�

��

��

�

� �

�

�

2

2

2 2

(36)

-

(37)

(38)

(39)

(40)

(41)

2.3 . Recursive Levenberg-Marquardt Learningof the KFRNN

p

L L

k

L k

L k

L k kk d k

1 2

1

2

2

(

(

(

( (( (

max

DY A k = D k V k

D k = F ' Y k

DY A k = D k X k

DY B k = D k U k

DY D k = D k Y k

D k = G ' Z k C D k

DY W k = DY C k DY A k DY B kDY A k DY D k

P k k P k P kW k S W k W k P k

S W k k k W k P k W k

W k

k

k P

X k+ = AX k + BU k

B = B B U = U U

[ ( )] ( ) ( )

( ) [ ( )]

[ ( )] ( ) ( )

[ ( )] ( ) ( )

[ ( )] ( ) ( )

( ) [ ( )] ( )

[ ( )] [ ( ( )), ( ( )), ( ( )),( ( )), ( ( ))]

( ) = ( ){ ( 1) ( 1).[ ( )] [ ( )] [ ( )] ( 1)}

[ ( )] = ( ) ( ) [ ( )] ( 1) [ ( )]

[ ( )] = ;

( ) = ; 10 10 ;

0,97 ( ) 1; 10 (0) 10

(.)

( 1) ( ) ( )

[ ; ]; [ ; ]

2 1,

1,

1 2,

2,

2,

2, 1,

2

1

1 0 1 2

ij i j

i i

ij i j

ij i j

ij i j

i i i i i

ij ij ij

ij ij

(42)

(43)

(44)

(45)

(46)

(47)

(48)

(49)

(50)

This section is dedicated to the topology, the BP andthe L-M algorithms of RTNN learning. The RTNN could beobtained from the KFRNN removing the output local andglobal feedbacks. The RTNN was used as a feedback/feed-forward controller.

The RTNN model and its learning algorithm of dynamicBP-type, together with the explanatory figures and stabi-lity proofs, are described in [6], [7], so only a short des-cription will be given here. The RTNN topology, derived invector-matrix form, was given by the following equations:

(53)

(54)

Therefore, the Jacobean matrix could be formed as:

The matrix was computed recursively by theequation:

Where the , and matrices were given as follows:

(51)

The matrix had dimension , whereas thesecond row had only one unity element (the others werezero). The position of that element was computed by:

(52)

After this, the given up topology and learning wereapplied for the CSTR system identification.

P k

S

Nw

i = k nw + ; k > nw

( )

(.) (.)

( x2)

mod ( ) 1

� � � �

� � �

� � ��

�

� � � �

� � � � �

�

�

�

� � �

1

1

1 4 6

3 6

T

T

T

T T T

�

3. Recurrent Trainable NN

3.1. Topology of the RTNN


Articles40

VOLUME 4, N° 4 2010

� � � � �

* * *

**

� � � �� max�max �max

1 11� 1�

2 2< � <

5

i=1

�

�W W = W k( )

�Y W kT[ ( )]0

01

�

0

01� �

A = Ai |Ai| <

Z k = G X k

C = C C Z = Z ; Z

V k = CZ k

Y k = F V k

X, Y, UN, L, M+1 Z

LZ U N M

Z = U = V L

T A N NB C N M L N

B C NL

F G

A X

N=L+M

E k = Y k - Y(k); E k = F' Y k E k

C k = E k Z k

E k = G' Z k E k ; E k = C k E k

B k = E k U k

A k = E k X k

Vec( A k ) = E k X k

A, B, CA, B C E, E , E

E X F G

vA

block-diag ( ), 1

( ) [ ( )]

[ ; ]; [ ]

( ) ( )

( ) [ ( )]

( )( +1)

( x1) ( x1)

-1, -1 ( x1)

( x )[ x( +1)] [ x( +1)]

( x1)( x1)

[.], [.] (.) (.)

( ) ( ) ( ) [ ( )] ( )

( ) ( ) ( )

( ) [ ( )] ( ) ( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

'(.) '(.)

[-1, 1]

(55)

(56)

(57)

(58)

(59)

Where: are vectors of state, output, and augmen-ted input with dimensions , respectively,is an dimensional input of the feedforward outputlayer, where and are the output andinput of the hidden layer; the constant scalar thresholdentries are , respectively; is apre-synaptic activity of the output layer; the super-index

means vector transpose; is block-diagonalweight matrix; and are and -augmented weight matrices; and are and

threshold weights of the hidden and output layers;are vector-valued tanh or sigmoid -activa-

tion functions with corresponding dimensions. Equation(55) represents the local stability condition imposed onall blocks of . The dimension of the state vector of theRTNN is chosen using the simple rule of thumb which is:

.

The same general BP learning rule (19) was used here.Following the same procedure as for the KFRNN, it waspossible to derive the following updates for the RTNNweight matrices:

(60)

(61)

(62)

(63)

(64)

(65)

Where are weight corrections of the of thelearned matrices , and , respectively; , and

are error vectors; is a state vector; and arediagonal Jacobean matrices, whose elements are deriva-tives of the tanh activation functions (see equations (21)and (26)). Equation (64) represents the learning of thefull feedback weight matrix of the hidden layer. Equation(65) gives the learning solution when this matrix is dia-gonal , which is the present case. The initial values ofthe weight matrices during the learning are chosen asarbitrary numbers inside a small range. The stability of theRTNN model used as a direct controller is assured by theactivation functions bounds and by the local sta-bility weight bound condition given by (55). The stabilityof the RTNN movement around the optimal weight pointhas been proved by one theorem (see the Ph.D. thesis of

1

1 0 1 2

1 1

2 2

0 0

1

1

3 2 2 1

3

3

3

1 2

3

T T T

T

T

T

T

3.2. BP Learning of the RTNN

d

�

Mariaca [7] for more details).Theorem of stability of the BP RTNN used as a direct

system controller [7]: Let the RTNN with Jordan CanonicalStructure is given by equations (53)-(59) and thenonlinear plant model is given by (31), (32). Under theassumption of RTNN identifiability made, the applicationof the BP learning algorithm for , ingeneral matricial form, described by equation (19), (63)-(65) without momentum term, and the learning rate(here it is considered as time-dependent and normalizedwith respect to the error) are derived using the followingLyapunov function:

(66)

Where: and are given by:

Where:

are vectors of the estimation error and anddenoted the ideal neural weight and the

estimate of the neural weight at the k-th step, respec-tively, for each case.

Let us define: , and, where , and, where is a vector composed by all

weights of the RTNN, used as a system controller, andis an Euclidean norm in .

Then the identification error is bounded, i.e.:

(67)

(68)

Where the condition for fulfillment is thatthe maximum rate of learning is inside the limits:

and for , we have:

(69)

Note that changes adaptively during the learningprocess of the network, where:

Here all: the unmodelled dynamics, the approximationerrors and the perturbations, are represented by the-term, and the complete proof of that theorem and the

rate of convergence lemma, are given in [7].

The general recursive L-M algorithm of learning [5],

A B C

k

L k = L k + L k

L k L k

A , B , CA , B , C

kk k k k k

k k

L k+ = L k+ + L k+ <

L k+ = L k+ L k

L k+

L k+

L k+ e k+ + k+

=

(.), (.), (.)

( )

( ) ( ) ( )

( ) ( )

( )( )

( )( ) ( ) ( ) ( ) ( )

( ) ( )

( 1) ( 1) ( 1) 0

( 1) ( 1) ( )

( 1) < 0

( 1) < 0

( 1) < ( 1) ( 1)

max({ }

�

�

�

��

�

� � � �

� �

�

1 2

1 2

( ) ( ) ( )

1 2

1

2

2

k k k

k

k

i

n

3.3. Recursive Levenberg-Marquardt Learningof the RTNN

� ��

��

� �

�

�

�

max max

max

max

max

= max =max = /= /

o Wy u W

2


Articles 41

VOLUME 4, N° 4 2010

0 < <�max2

� �2 2max max

—

T

T

T

L k e k1( ) = ( )212

( ) = tr ( ) + tr ( ) +L k W W W W2 ( ) ( ) ( ) ( )A k A k B k B k

tr ( )W WC k C k( ) ( )

W A A W B B W C CA k k B k k C k k( ) ( ) ( ) ( ) ( ) ( )= = =� � � � ��

* **

� ��

* * *

3

i=1


Articles42

[7], [8] is given by equations (37)-(40), where is thegeneral weight matrix under modification;is the RTNN output vector; is an error vector; is theplant output vector. Using the RTNN adjoint block dia-gram [5], it was possible to obtain the values of foreach updated weight propagating . Applying equa-tion (40) for each element of the weight matrices

, the corresponding gradient components are ob-tained as:

(70)

(71)

(72)

(73)

(74)

Therefore the Jacobean matrix could be formed as:

(75)

The matrix was computed recursively by equa-tions (49)-(52). Next, the given up RTNN topology andlearning were applied for CSTR system control.

This section is dedicated to the design of direct andindirect (sliding mode) adaptive control system using theKF RNN as a nonlinear plant identifier. The RTNN was usedas a feedback/feedforward controller in the case of directadaptive neural control.

This section described the direct adaptive controlusing KFRNN as plant identifier and RTNN as a plant con-troller (feedback / feedforward). The block-diagram ofthe control system is given in Fig. 3. The following studydescribed the linearized model of that closed-loop con-trol system.

Let us present the following z-transfer function repre-sentations of the plant, the state estimation part of theKFRNN, and the feedback and feedforward parts of theRTNN controller:

WA, B, C Y

E Y

DYD=I

A,B, C

DY C k = D k Z k

D k = F ' Y k

DY A k = D k X k

DY B k = D k U k

D k = G ' Z k C D k

DY W k = DY C k DY A k DY B k

k

( )

[.]

()

[ ( )] ( ) ( )

( ) [ ( )]

[ ( )] ( ) ( )

[ ( )] ( ) ( )

( ) [ ( )] ( )

[ ( )] [ ( ( )), ( ( )), ( ( ))]

P( )

p

ij i j

i i i

ij i j

ij i j

i i i i i

ij ij ij

1,

1,

2,

2,

2, 1,

4. Adaptive Control Systems Design

4.1. Direct Adaptive Neural Control Scheme

Fig. 3. Block-diagram of the closed-loop neural controlsystem.

W z = C zI A B

P z = zI A B

Q z = C zI A B

Q z = C zI A B

Y z = W z I Q z P z Q z R z z

z = W z z z

z

E k = Y k Y k k

E k = R k Y k k

p p p p

i i i

c c c

c c c

p p i

p

i p

c p

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )[ + ( ) ( )] ( ) ( )+ ( )

( ) ( ) ( )+ ( )

( )

( ) ( ) ( ) 0;

( ) ( ) ( ) 0;

�

�

�

�

�

� � �

�

� !

� !

�

�

�

�

�

1

1

1

1

1

(76)

(77)

(78)

(79)

The control systems z-transfer functions (76)-(79)are connected by the following equation, which is deri-ved from Fig. 3, and is given in z-operational form:

(80)

(81)

Where: represented a generalized noise term. TheRTNN and the KFRNN topologies were controllable andobservable, and the BP algorithm of learning was conver-gent, [5], [7], so the identification and control errorstended to zero:

(82)

(83)

This means that each transfer function given by equa-tions (76)-(79) was stable with minimum phase. The clo-sed-loop system was stable and the feedback dynamicalpart of the RTNN controller compensated the plant dyna-mics. The feedforward dynamical part of the RTNN con-troller was an inverse dynamics of the closed-loop systemone, which assured a precise reference tracking in spiteof the presence of process and measurement noises.

The indirect adaptive control using the RTNN as plantidentifier has been described in, [5]. Later the proposedindirect control has been derived as a Sliding Mode Con-trol (SMC) and applied for control of unknown hydrocar-bon biodegradation processes, [6], using the KF RNNidentifier with BP learning. Here we applied the KF RNNidentifier with L-M learning. The block diagram of the in-direct adaptive control scheme is shown in Fig. 4. It con-tains identification and state estimation KF RNN anda sliding mode controller.

The stable nonlinear plant is identified by a KF RNNmodel with topology, given by equations (10)-(18) lear-

1 1

2 2

1 2

1 2

4.2. Indirect Adaptive Control Scheme(Sliding Mode Control)

Fig. 4. Block diagram of the closed-loop system containingKF RNN identifier and a SMC.

VOLUME 4, N° 4 2010


Articles 43

ned by the stable BP-learning algorithm, given by equa-tions (19)-(30), or using the second order LM-learningalgorithm, given by equations (37)-(52). The simplifica-tion and linearization of the neural identifier equations(10)-(18), omitting the term, leads to the nextlocal linear plant model, extracted from the complete KFRNN model:

(84)

(85)

Where is the derivative of the activation functionand , is supposed.

In [12], the sliding surface is defined with respect tothe state variables, and the SMC objective is to move thestates form an arbitrary space position to the sliding sur-face in finite time.

In [13], the sliding surface is also defined with res-pect to the states but the states of the SISO systems areobtained from the plant outputs by differentiation. In[14], the sliding surface definition and the control objec-tives are the same. The equivalent control systems designis done with respect to the plant output, but the reacha-bility of the stable output control depended on the plantstructure.

In [6], the sliding surface is derived directly with res-pect to the plant outputs which facilitated the equivalentSMC systems design. Let us define the following slidingsurface equation as an output tracking error function:

(86)

Where: is the Sliding Surface Error Function (SSEF)defined with respect to the plant output; is the sys-tems output tracking error; are parameters of the desi-red stable SSEF; is the order of the SSEF. The trackingerror in two consecutive moments of time is defined as:

(87)

Where are L-dimensional reference and out-put vectors of the local linear plant model. The objectiveof the sliding mode control systems design is to finda control action which maintains the systems error on thesliding surface which assure that the output tracking er-ror reaches zero in steps, where . So, the controlobjective is fulfilled if:

(88)

Now, let us to iterate (85) and to substitute (84) in itso to obtain the input/output local plant model, whichyields:

(89)

From (86)-(87), and (89) it is easy to obtain:

(90)

DY

X k+ = A X k + BU k

Z k = HX k H = CG' Z

GL = M

S k+ = E k+ + E k i+

SE

p

S k+ = R k Z kE k+ = R k+ Z k+

R k Z k

P P < N

S k+ =

Z k+ = FX k+ = F AX k BU k

R k+ Z k+ + E k i+

(.)

( 1) ( ) ( )

( ) ( ); ( )

'(.)

( 1) ( 1) ( 1); < 1

(.)(.)

( 1) ( ) ( );( 1) ( 1) ( 1)

( ), ( )

( 1) 0

( 1) ( 1) [ ( ) + ( )]

( 1) ( 1) ( 1) = 0

1

"# � #

#

�

�

� "# �

i

i

i

The substitution of (89) in (90) gives:

(91)

As the local approximation plant model (84), (85), iscontrollable, observable and stable (see [6], [7]), thematrix is diagonal, and , then the matrix pro-duct (HB), representing the plant model static gain, isnonsingular, and the plant states are smooth non-increasing functions. Now, from (91) it is easy to obtainthe equivalent control capable to lead the system to thesliding surface which yields:

(92)

Following [12], the SMC avoiding chattering is takenusing a saturation function instead of sign one. So theSMC takes the form:

(93)

The SMC substituted the multi-input multi-outputcoupled high order dynamics of the linearized plant withdesired decoupled low order one.

The CSTR model given in [9], [10] was chosen as anexample of RNN applications in system identification andcontrol of biotechnological plants. Numerical values forthe parameters and nominal operating conditions of thismodel are given in Table 1.

The CSTR is described by the following continuoustime nonlinear system of ordinary differential equations:

(94)

(95)

R k+ FAX k FBU k + E k i+

A L = M

X k

U k FB FAX k +R k+ + E k i+

U* k

C C t k C t

( 1) ( ) ( ) ( 1) = 0

( )

( ) = ( ) ( ) ( 1) ( 1)

( ) =

= ( ( )) ( )exp

� � "# �

� "# �

� � �

i

eq i

1

0

�1

5. Description of the CSTR Bioprocess Plant

Table 1. Parameters and operating conditions of the CSTR.

Af A A

VOLUME 4, N° 4 2010

P

P

P

P

i=1

i=1

i=1

i=1

U keq( ) =

� � � � � $U U k U k U k U% %eq eq eq( )/ ( ) if ( )

if ( ) � � &U k Ueq %

ParametersQ

C

V

= (L/min)=1.0 (mol/L)

T = T = 350 (K)= (L)

= 9.95x10 (K)= 2x10 (cal/mol)

C

E/RH

3

5�

Af

f f

Parameters�� = 1000 (g/L)

= 1 (cal/gK)= 103.41 (L/min)

= 7x10 (cal/min K)T = 440.2 (K)= 7.2x10 (l/min)

C CQ

hA

k

p p

e0

0

0

5

10

c

c

dC tA( )

dT t( ) = ( ( )) expT T t� � �f

Q t T T tc( ) 1 exp ( ( ))� �ef

Q

Q

E

E

�hA

( ) ( )�H C tA

�c pcC C t( )A

dt

dt

V

V

RT t( )

RT t( )

Q tc c pc( )� C

�Cp

�CpV


Articles44

In this model it is enough to know that within theCSTR, two chemicals are mixed and that they react inorder o produce a product compound at a concentration , and that the temperature of the mixture is

. The reaction is exothermic and it produces heatwhich slows down the reaction. By introducing a coolantflow-rate , the temperature can be varied and hencethe product concentration can be controlled. Here isthe inlet feed concentration; is the process flow-rate;

and are the inlet feed and coolant temperatures,respectively; all of which are assumed constant at nominal values. Likewise, , , , , , , , andare thermodynamic and chemical constants related tothis particular problem. The quantities , , and ,shown in Table 1, are steady values for a steady operatingpoint in the CSTR. The objective was to control the product compound by manipulating . The operatingvalues were taken from [9] and [10], where the performance of a control system is reported.

Some simulation results of the CSTR biotechnologicalplant neural identification and control are summarized inthis part.

A -C t

T t

Q tC

QT T

-k E/R V H C C

Q T C

-A Q t

-NN

( )( )

( )

( )

e

� �

6.

A

c

Af

f f

pc p c

c A

c

0

0 0 0

Simulation Results

6.1. Simulation Results of Bioprocess PlantNeural Identification

Results of detailed comparative graphical simulationof CSTR KFRNN plant identification by means of the BPand the L-M learning are given in Fig. 5 and Fig. 6. A 10%white noise with different variance (SEED parameter) foreach run was added to the plant inputs and outputs andthe behavior of the plant identification was studied accumulating some statistics of the final MSE% ( ) for KFRNNBP and L-M learning. The results for 20 runs are given inTables 3 and 4.

The mean average cost for all runs ( ) of KFRNN plantidentification, the standard deviation ( ) with respect tothe mean value, and the deviation ( ) are presented inTable 2 for the BP and L-M algorithms. They were computed by the formulas:

(96)

The numerical results given in Tables 2, 3, and 4 areillustrated by the bar-graphics in Figures 7a)and b).

-

-

'

(

)

av

VOLUME 4, N° 4 2010

Fig. 5. Graphical results of identification using BP KFRNN learning. a) Comparison of the plant output (continuous line)and KFRNN output (pointed line); b) state variables; c) comparison of the plant output (continuous line) and KFRNNoutput (pointed line) in the first instants; d) MSE% of identification.

( "' ��) " �� ' � (= = =avk av1 21n in

Fig. 6. Graphical results of identification using L-M KFRNN learning. a) Comparison of the plant output (continuous line)and KFRNN output (pointed line); b) state variables; c) comparison of the plant output and KFRNN output in the firstinstants; d) MSE% of identification.

n

k=1


Articles 45

Table 2. Standard deviations and mean average values ofidentification validation using the BP and L-M algorithms ofKF RNN learning.

Table 3. MSE% of 20 runs of the identification programusing the KFRNN BP algorithm.

Table 4. MSE% of 20 runs of the identification programusing the KFRNN L-M algorithm.

The comparative results showed inferior MSE%, , andfor the L-M algorithm with respect to the BP one.

The graphical simulation results of DANC using the L-Malgorithm of learning are presented in Fig.8 where thefinal MSE% was 0.854% for the L-M algorithm of learning.Similar results are given on Fig.9 for the indirect SMC con-trol. The final value of the MSE% obtained for the indirectSMC using the L-M algorithm of learning for the KFRNNidentifier is of 0.434%.

The graphical results and the obtained final MSE%showed that the indirect SMC control is about twice timesmore precise that the DANC due to the utilization of theestimated states and parameters in that case, and alsodue to the SMC algorithm of control which substitute theplant dynamics by a decoupled lower order one.

This paper proposed a new KFRNN model for systemidentification and state estimation of nonlinear plants.The KFRNN is learnt by the first order BP and by the se-cond order L-M recursive learning algorithms. The valida-ting results of system identification reported here gavepriority of the L-M algorithm of learning over the BP onewhich is paid by augmented complexity. The estimatedstates and parameters of the plant, obtained by this Kal-man filter recurrent neural network model are used fordirect and indirect adaptive trajectory tracking controlsystem design. The applicability of the proposed neural

(

)

6.2. Simulation Results of Bioprocess PlantAdaptive Neural Control

7. Conclusions

VOLUME 4, N° 4 2010

BP algorithm(

)

= 0.9457= 0.0416

NoMSE%

NoMSE%

NoMSE%

NoMSE%

NoMSE%

NoMSE%

NoMSE%

NoMSE%

10.9559

60.9444

110.8523

160.9688

10.8123

60.8072

110.8659

160.8628

20.9654

70.9591

120.8105

170.8630

20.8001

70.8072

120.8105

170.8226

30.8821

80.9700

130.9863

180.8624

30.8553

80.8285

130.8269

180.8514

40.9614

90.9685

140.9038

190.8521

40.8360

90.8236

140.8218

190.8288

50.8798

101.0034

151.0122

200.8898

50.8149

100.8037

150.8118

200.8280

L-M algorithm(

)

= 0.8264= 0.0188

Fig. 7. Comparison between the final MSE% for 20 runs of the identification program: a) using BP algorithm of learning,b) using L-M algorithm of learning.

Fig. 8. Detailed graphical simulation results of CSTR plant DANC using L-M learning. a) comparison between the plantoutput and the reference signal; b) comparison between the plant output and the reference signal in the first instants;c) control signal; d) MSE% of control.


Articles46

control system, learnt by the BP and L-M algorithms, wasconfirmed by simulation results with a CSTR plant. Theresults showed good convergence of the two algorithmsapplied. The graphical and numerical validation identifi-cation results showed that the L-M algorithm of learningis more precise but more complex then the BP one. Thecontrol results of DANC and IANC (SMC) showed a greatprecision of reference tracking (the final MSE% is 0.854%for the DANC and 0.434 for the indirect SMC). The betterresults obtained with the indirect SMC are due to the uti-lization of the estimated states and parameters in thatcase, and also due to the SMC algorithm of control whichsubstitute the plant dynamics by a decoupled lower orderone.

-Department of Automatic Control, CINVESTAV-IPN,Av. IPN No 2508, 07360 Mexico City, Mexico. Phone:(+52-55)5747-3800/ext. 42-29. E-mails:{baruch;cmariaca}@ctrl.cinvestav.mx.* Corresponding author

ACKNOWLEDGMENTS

AUTHORSIeroham Baruch*, Carlos-Roman Mariaca-Gaspar

References

The graduated Ph.D. student Carlos-Roman Mariaca-Gaspar isthankful to CONACYT for the scholarship received during hisstudies at the Department of Automatic Control, CINVESTAV-IPN, MEXICO.

[1] Narendra K.S., Parthasarathy K., “Identification andControl of Dynamical Systems Using Neural Networks”,

, vol. 1, no. 1,1990, pp. 4-27.

[2] Hunt K.J., Sbarbaro D., Zbikowski R., Gawthrop P.J.,“Neural Network for Control Systems (A survey)”,Automatica 28 (1992), pp. 1083-1112.

[3] Haykin S.,, Second Edition, Section 2.13, 84-89; Section 4.13,

208-213. Prentice-Hall, Upper Saddle River, New Jersey7458, 1999.

IEEE Transactions on Neural Networks

Neural Networks, a Comprehensive Founda-tion

[4] Sage A.P., , Prentice-Hall Inc.,Library of Congress Catalog Number 68-20862, Engle-wood Cliffs, New Jersey, 1968.

[5] Baruch I. S., Mariaca-Gaspar, C. R., “A Levenberg-Mar-quardt Learning Applied for Recurrent Neural Identifi-cation and Control of a Wastewater Treatment Biopro-cess”, ,Wiley Periodicals, Inc., vol. 24, 2009, pp. 1094-1114.

[6] Baruch I.S., Mariaca-Gaspar C.R., Barrera-Cortes J.,“Recurrent Neural Network Identification and AdaptiveNeural Control of Hydrocarbon Biodegradation Proces-ses. In: Hu Xiaolin, Balasubramaniam P. (eds.), -

, I-Tech Education and PublishingKG, Vienna, Austria, ISBN 978-953-7619-08-4, 2008,Chapter 4, pp. 61-88.

[7] Mariaca Gaspar C.R.,-

, Ph. D. Thesis (in Spanish), Baruch,I.S., Martinez-Garcia, J.C. (thesis directors), Depart-ment of Automatic Control, CINVESTAV-IPN, MexicoCity, 3 July 2009.

[8] Ngia L.S., Sjöberg J., “Efficient Training of Neural Netsfor Nonlinear Adaptive Filtering Using a Recursive Le-venberg Marquardt Algorithm”,

, vol. 48, 2000, pp. 1915-1927.[9] Zhang T., Guay M., “Adaptive Nonlinear Control of Con-

tinuously Stirred Tank Reactor Systems”. In: -, Arlington, 25 -

27 June, 2001, pp. 1274-1279.[10] Lightbody G., Irwin G.W., “Nonlinear Control Structures

Based on Embedded Neural System Models”,, no. 8, 1997, pp. 553-557.

[11] Wan E., Beaufays F., “Diagrammatic Method for Derivingand Relating Temporal Neural Network Algorithms”,

, vol. 8, 1996, pp. 182-201.[12] Young K. D., Utkin V.I., Ozguner U., “A Control Engine-

er's Guide to Sliding Mode Control”,7 (3), 1999, pp. 328-342.

[13] Levent A., “Higher Order Sliding Modes, Differentiationand Output Feedback Control”,

(Guest Editor: FridmanL.M.) ISSN 0020-7179, vol. 76, no. 9/10, 15 June-10

Optimum Systems Control

International Journal of Intelligent Systems

Recurrent Neural Networks

Topologies, Learning and Stabilityof Hybrid Neural Networks, Applied for Nonlinear Biotechnological Processes

IEEE Trans. on SignalProcessing

Proceedings of the American Control Conference

IEEE Trans.on Neural Networks

Neural Computations

IEEE Transactionson Control Systems Technology

International Journal ofControl, Special Issue Dedicated to Vadim Utkin on theOccasion of his 65 Birthday

,

rd

th

th

th th

th

VOLUME 4, N° 4 2010

Fig. 9. Detailed graphical simulation results of CSTR plant Sliding Mode Indirect Control using L-M KFRTNN learning.a) comparison between the plant output and the reference signal; b) comparison between the plant output and thereference signal in the first instants; c) control signal; d) MSE% of control.


Articles 47

July 2003, pp. 924-941.[14] Eduards C., Spurgeon S.K., Hebden, R.G., “On the

Design of Sliding Mode Output Feedback Controllers”,

(GuestEditor: Fridman L.M.) ISSN 0020-7179, vol.76, no.9/10, 15 June-10 July 2003, pp. 893-905

Let the Extended Recurrent Trainable Neural Network withJordan Canonical Structure given by (1), (2), (3), (4), (5), (6),(7) and the nonlinear plant model as follows:

(A.1)(A.2)

and the plant and activation functions fulfill the followingassumptions:

The plant dynamics is locally Lipchitz, so thenonlinear functions , are as:

and , are modeling errors, which reflex the effect ofunmodelled dynamics.

The activation functions have the followingTaylor approximation:

with the approximation error bound given by:

and the output signal error is defined by:

Now, let us define the state estimation error, add and subtractthe RTNN to the last equation and apply the Assumption 2,then:

Let us now define the output identification error and put it interms of the state estimation error as:

International Journal of Control, Special Issue Dedicatedto Vadim Utkin on the Occasion of his 65 Birthday

,

th

th th

x k f x k v ky k h x k

f h

f f f f f f f x kh h h h h h h x k

f h

e k y k y k

k x k x k

( +1) = [ ( ), ( )]( ) = [ ( )]

( ) ( )

: = { = , ( ) }: = { = , ( ) }

( ) = ( ) ( )

( ) = ( ) ( )

Assumption 1:

Assumption 2:

� �

� )� � � � � � �

� )� � � � � � �

�

�

0 1

0 1

Appendix A: Stability proof of the theorem for KF RNNtopology and BP learning.

Where: the term ; the are the higherorder terms in the Taylor series approximation;

is the unmodeled dynamics; is an offset.If Assumptions 1 and 2 fulfill, the learning algorithm for theRTNN is given by (8) and the learning parameters , arenormalized and depended on the output error structure.Then, the approximation error is bounded.Consider a Lyapunov candidate function as:

(A.3)

In which and are given by:

(A.4)

(A.5)

Where: are vectors of the estimation error anddenoted the ideal neural

weight and the estimate of neural weight at the k-th step,respectively, for each case.Let us consider the equation (A.4). The change of the Lyapunovfunction in two consecutive samples due to the training processis obtained by:

(A.6)

Then, defining as the difference between two consecu-tive error samples, then the equation (A.6) becomes:

(A.7)

Where: can be defined as:

(A.8)

Putting all weights into one vector as

(A.9)

Where:,,

,,

which represents the weight vectors constructed by theircolumns. Also let:

(A.10)

u k u k Oh x k u k

u k O O

L k L k L k

L k L k

L k e k

L k L k+ L k e k+ e k e k

e k+ e k

e k

L k e k e k e k

e k W

W

( ) = ( ) +( ( ), ( ))

= ( ) +

( ) = ( ) ( )

( ) ( )

( ) = ( )

( ) = ( 1) ( ) = [ ( 1) ( )][ ( )+

+ ( 1) ( )]

( )

( ) = ( )[ ( )+ ( )]

( )

= [[ ] [ ] [ ] [ ] [ ] ]

= [[ ] [ ] [ ] ]= [[ ] [ ] [ ] ]

= [[ ] [ ] [ ] ]= [[ ] [ ] [ ] ]= [ ]

F

F F

k k

�

� �

�

� �

�

*

1,2,3,4

1 2

1 2

1

1 2

1 1

1 1 1

1

1 2

1 1 1 1

2 21 22 2

1 2

1 2

1

2

T T T T T T

T T T

T T T

T T T

T T T

T

n n n

l

m

n

() ( )

A , A , B , C ,D A , A , B , C , D

A A B C D

A A A AA A A AB B B BC C C CD D

and ( ) ( ) ( ) ( ) ( )k k k k k

�

�

�

�

VOLUME 4, N° 4 2010

12

� � � ��

* * * *

*

1

1

�e k( )�W

12

2

2


Articles48

Where: and represented the learning rate matrices, the momentum rate matricescorresponding to the matrix weights , respectively, and

. Moreover, and aretwo positive constants, and is an identity matrix, where the general symbol is substituted by , respectively. We coulddefine as:

(A.11)

(A.12)

(A.13)

Let:

(A.14)

Then:

(A.15)

and

(A.16)

Proposing: , then:

(A.17)

According to the Lyapunov stability theory, if convergence must be guaranteed, then , thus , and:

(A.18)That is:

(A.19)Let: . Thus, as long as:

(A.20)

( , , , , ) ( , , , , )( )

( = 1,...,5) ( = 1,...,5)

=

= 1

( 1) < 0 2 +4 1> 0

= max { }

� � � � � � � � � �

� �

� + ,�� + �-,

. #�

� # #�

� �

A A B C D A A B C D1 2 1 2

2

A , A , B, C, Di i

I Z A , A , B, C, DW

W W k W k

L k+

1 2

1 2

i i

Z

imax

..................................................................................

VOLUME 4, N° 4 2010

12

12

12

12

12

�# �.e k+ e k+ e k( 1) = ( 1) ( )

� #�# #� . .L k+ e k+ e k+ e k+ e k+ e k+ e k e k1( 1) = ( 1)[ ( 1)+ ( 1)] = ( 1)[2 ] + ( 1) ( )[ 1] + ( )2 2 2 2

� � # #� � . L k+ e k+ e k1( 1) = ( 1)[ 2 +4 1] [ ( )]2 2 2 2

11�/2

1

3

1�/2&�#�&

i=1


Articles 49

Note that is the Euclidean norm, therefore:

(A.21)

Now let: , and , then:

(A.22)

Now, working with equation (A5), we have:

If we consider the change of the Lyapunov function in two consecutive samples due to the training process, we obtain:

(A.23)Now substituting the following quantities:

We could obtain:

(A.24)

And if the updated learning law is given by (19), then:

�+ , � � * ��+ ,� k k= = maxmax k

VOLUME 4, N° 4 2010

�e k( ) �y k( )�W �W

11�/2

11�/2

&�� &max�max �max


Articles50

Now we could use the followings trace properties:

Note that is the Euclidean norm, is a constant and are weight matrices. Then:

So, due to the learning matrix law given by the equations (19)-(29), and collecting the errors as a common factor, using trace properties,we can rewrite as:

tr AB tr BA tr A tr B tr C tr A+B+C AB B A tr AA tr A A Atr A tr A tr A tr A

A , A , B, C, D

L k

( ) = ( ); ( )+ ( )+ ( ) = ( ); ( ) = ; ( ) = ( ) = ;( ) = ( ); ( ) = ( )

( )

( )

T T T T T

T

� �

� �

��

22

2 1 2

2

VOLUME 4, N° 4 2010


Articles 51

Due to the error definition, collecting and put the following equation as a function of , we get:

First and second traces gave us four terms as:

, and

Using the following inequality [6], [7]: , which is valid for any , and for any positive defi-nite matrix , we obtained:

Analyzing term by term and applying the Rayleigh inequality:

we could obtain:

e k( )

VOLUME 4, N° 4 2010


Articles52

Now, making inner terms equal to one as in the unit circle condition for discrete time, as:

At last we get the final condition:

(A.25)

Where: the unmodeled dynamics and/or perturbations term is given by:

(A.26)

Applying the Lemma of the KF RNN rate of convergence, [6], [7], for the result (A.26) we could conclude that: the - term must bebounded by the weight matrices and the learning parameter, in order to obtain the final result:

As a consequence:From equations (A.22) and (A.25) we easily could get the equation (20). Therefore the boundedness of the is guaranteed.

Applying the limit's definition, the identification error bound condition is obtained as:

Starting from the final result of the Theorem of BP KF RNN stability:

After an analysis of the iterations from , we get:

Dividing by and applying the limit's definition, the identification error bound condition is obtained in the final form:

From here we could see that the term must be bounded by weight matrices and the learning parameter, in order to obtain:

d k

d

k

k

d

( )

=0

Lemma of KF RNN rate of convergence.

Proof.

VOLUME 4, N° 4 2010

Abstract:

1. Introduction

-

Fuzzy logic controllers are used successfully in manyapplication areas, and these include control, classification, etc. [1],[2],[3],[4],[5],[6],[7]. These systems based on rules incorporate linguistic variables, linguisticterms and fuzzy rules. The acquisition of these rules is notan easy task for the expert and is of vital importance inthe operation of the controller.

The process of adjusting these linguistic terms andrules is usually done by trial and error, which impliesa difficult task, and for this reason there have been methods proposed to optimize those elements that overtime have taken importance, such as genetic algorithms[8],[9],[10].

A Genetic Algorithm (GA) [9],[10] is a stochastic optimization algorithm inspired by the natural theory ofevolution. From a principle proposed by Holland [9], GAshave been used successfully to manage a wide varietyproblems such as control, search, etc. [11].

This paper proposes a novel method for genetic optimization of the triangular and trapezoidal membership

This paper proposes a novel method for genetic optimization of triangular and trapezoidal membership functionsof fuzzy systems, for hardware applications such as theFPGA (Field Programmable Gate Array). This method consists in taking only certain points of the membership functions, with the purpose of giving more efficiency to thealgorithm. The genetic algorithm was tested in a fuzzy controller to regulate engine speed of a direct current (DC)motor, using the Xilinx System Generator (XSG) toolbox ofMatlab, which simulate VHDL (Very High Description Language) code.

--

-

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--

-

-

-

Keywords: genetic algorithms, fuzzy, controller, Matlab,Simulink, Xilinx System Generator, VHDL, FPGA.

functions of a fuzzy logic system for hardware applications such as FPGA (Field Programmable Gate Array). Thismethod involves taking only a small number for points ofthe membership functions in order to give greater efficiency to the algorithm. The GA has been tested in a fuzzylogic controller to regulate the speed engine direct current (DC) using the Matlab [12] platform and XSG [13]with good results.

This paper is organized as follows: in section 2 wepresent an introductory explanation of Genetic Algorithms, Fuzzy Inference Systems and FPGAs, section 3describes the novel method for genetic optimization ofmembership functions for FLC in FPGAs, the test andresult the novel genetic optimization of membership functions for FLC for speed regulate the motor DC are shownin section 4. Finally, section 5 presents the conclusions

The Genetic Algorithm is an optimization and searchtechnique based on the principles of genetics and naturalselection. A GA allows a population composed of manyindividuals to evolve under specified selection rules toa final state that maximizes the “fitness” (i.e. minimizesthe cost function) [14].

A GA is inspired by the mechanism of natural selection where stronger individuals are likely the winners ina competitive environment. Here the GA uses a direct analogy of such natural evolution. Through the genetic evolution method, an optimal solution can be found and represented by the final winner of the genetic game [15].

Throughout a genetic evolution, the fitter chromosome has a tendency to yield good quality offspring, whichmeans a better solution to any problem. In a practical GAapplication, a population pool of chromosomes has to beinstalled and these can be initially randomly set. The sizeof this population varies from one problem to another. Ineach cycle of genetic operations, termed as an evolvingprocess, a subsequent generation is created from the

-

-

-

-

.

-

---

-

2. Preliminaries

NOVEL GENETIC OPTIMIZATION OF MEMBERSHIP FUNCTIONSOF FUZZY LOGIC FOR SPEED CONTROL OF A DIRECT CURRENT MOTOR

FOR HARDWARE APPLICATIONS IN FPGAS

Yazmin Maldonado, Oscar Castillo, Patricia Melin


Articles 53

Fig. 1. GA cycle.

chromosomes in the current population. This can onlysucceed if a group of these chromosomes, generally called “parents is selected a specific selection routine.The genes of the parents are mixed for the production ofoffspring in the next generation. It is expected that fromthis process of evolution, the better chromosome willcreate a larger number of offspring, and thus has a higherchance of surviving in the subsequent generation, emulating the survival of the fittest mechanism in nature.Figure 1 shows the GA cycle.

Of course, the GA is not the best way to solve everyproblem, GAs have proven to be a good strategy becauseof its optimal results in several areas of application [3],[16].

The GA has applications in a wide variety of fields todevelop solutions to complex problems, including optimization of fuzzy systems, offering them learning andadaptation, they are commonly called genetic fuzzy systems or fuzzy system hybrids.

Fuzzy systems have been used more and more, because they tolerate imprecise information and can be usedto model nonlinear functions of arbitrary complexity.A fuzzy system (FIS) consists of three stages: Fuzzification, Inference and Defuzzification [17]. We describebelow these stages.

Is the interpretation of input values(numeric) by the fuzzy system, and the obtained outputare fuzzy values.

Let be a linguistic variable anda fuzzy set associated with a linguistic value . The

translation of a numeric value corresponds to a linguistic value associated with a degree of membership,

, and this is known as Fuzzification. The membership degree represents a value of membershipto a fuzzy set [18].

Is basically like the brain of the system,here the rules of the form if-then that describe thisbehavior are used [2]. For example:

If is and and is Then is (1)

where are the inputs, are linguisticterms and is the output.

Defuzzification Consists in obtaining a numeric valuefor the output. This stage basically selects a point that isthe most representative of the action to perform [2]. There are several methods to calculate the Defuzzification,such as the Center of Height (COH), Center of Gravity(COG), etc. The COG is shown in Equation 2.

(2)

where is the maximum height of the consequent fromrule to rule [2].

In Figure 2, the fuzzy system information processingis illustrated.

-

-

-

-

-

-

-

-

-

via

Fuzzification:

Definition 1.

Inference:

x XT x

x A y

i

�

�

�

i )(

( )( )

Tx

x u xu x

x A B

x x A A , By

hN

i

Ti

Ti

n n

n n

�

�

1 1

1 1

1

Fig. 2. Fuzzy System.

A fuzzy system can be implemented on a general purpose computer, or by a specific use of microelectronicsrealization. The first offers a great versatility in terms ofease of development in various high level programs, thesecond device is performed in high scale integration,such as the ASICs [19].

The ASICs offer great advantages for high performance and price reduction is concerned, however, also havethe disadvantage of requiring a high level of productionof the same design to actually be affordable and time toget in the market is large relative to that of using a FPGA.

The applications of the FPGAs go beyond the simpleimplementation of digital logic. The FPGAs can be used toimplement specific architectures to accelerate a particular algorithm. Systems based on FPGAs provide betterperformance than their corresponding implementationsin software platforms for general use. A specific architecture for an algorithm can have a yield of 10 to 1000 timeshigher than an implementation on a DSP (Digital SignalProcessor). Applications that require a great number ofsimple operations are suitable for implementation onFPGA, a processing element can be designed to performthis operation and several instances of it can be played toperform parallel processing [20].

An FPGA is a semiconductor device that contains in itsinterior components such as gates, multiplexers, etc.These are interconnected with each other, according toa given design. These devices use the VHDL programminglanguage, which is an acronym that represents the combination of VHSIC (Very High Speed Integrated Circuit)and HDL (Hardware Description Language) [13].

Implementing an embedded fuzzy system on an FPGAis not as easy as it seems, since there are few appropriated design tools to achieve this task. Most of the time,the designer needs to construct every part of the inference system from scratch. Fortunately, there is an increasing interest in the development of designing platforms the easily achieve this task, such is the case of theXfuzzy 2.1 and Xfuzzy 3.0; however, at the present timethey cannot provide VHDL code for trapezoidal membership functions for arithmetic calculation. Other implementations of a FIS on an FPGA are reported in [21].

Any hardware implementation of an electronic systemrequires a complex methodology to test and validate every stage in the design process to guarantee its correctfunctionality; this is particularly true when the designerdecides to use a HDL to make a design.

The FPGAs are good platforms for fast prototyping ofdigital hardware. FPGAs are very effective in implementing FLSs since they allow fast modeling and hardwareverification. FPGAs can be programmed in the system,

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VOLUME 4, N° 4 2010

The basic elements of an FPGA are:1. Configurable logic blocks CLBs, and their structure

and content is called architecture. There are manytypes of architectures, which vary largely in complexity (from a simple door to more complex modules orSPLD-like structures). They often include bi-stable orMOS (Metal Oxide Semiconductor) to facilitate theimplementation of sequential circuits. Other important modules are the building blocks of I / O (IOB).

2. Interconnection resources, whose structure and content defines the routing architecture.

3. RAM, which is loaded during reset to configure andconnect blocks.

Figure 4 shows these elements.

Figure 5 shows the CHIP Spartan Basic Elements.

-

-

-

The fuzzy logic controller is coded in VHDL, the FLC forthe fuzzification stage, is able to instantly calculate thedegree of membership, using a method to calculate theslopes [23][24][25], the inference is working with themax-min [26][27][28] and the defuziffication with themethod of heights.

Figure 6 shows the block diagram in XSG of the FLC forthe regulation of speed of a DC motor, the system inputsare reset, error , error of change , and the parame-ters of each membership function for inputs and outputare in total 11. The system only has an output .

The FLC has two inputs and one output, each input andoutput contains three membership functions, two trape-zoidal one triangular. Figure 7 shows the triangular andtrapezoidal membership functions (MF) that are used.

For the optimization of the FLC using GAs, you mustdefine the chromosome that represents the informationof the individual, which in this case is related to theuniverse of discourse and the linguistic terms. Figure 8shows the chromosome of the GA.

Fig. 4. FPGA Basic Elements.

3. Novel Genetic Optimizationof Membership Functions for Fuzzy LogicController in FPGAs

e t e t

Y t

( ) '( )

( )

without shutting down the system. This functionalityallows modification and tuning of rules and-or fuzzifiersto achieve better control performance. In order to accelerate the design of FLS hardware, it is helpful to havea design environment, which allows algorithmic specification of the FLS and eases the automatic synthesis andverification of FLS hardware. The topic of FLS implementation onto FPGAs has been investigated by several researchers. A brief overview of the work done by someresearchers is presented next.

The design of an FPGA implementation is done byspecifying the logic function to develop, either by a CAD(computer aided design) or through a hardware description language. Having defined the function to perform,the design is transferred to the FPGA. This process program the configurable logic blocks (CLBs) to performa specific function (there are thousands of configurablelogic blocks in the FPGA). The configuration of theseblocks and their interconnections flexibility are the reasons why it can get very complex designs. The interconnections enable connecting the CLBs. Finally, it has configuration memory cells (CMC, Configuration MemoryCell) distributed throughout the chip, which store allinformation necessary for programming programmableelements mentioned. These cells usually consist of configuration RAM and are initialized in the process of loading of the configuration [22]. The programmable elements of an FPGA are:1. Configurable Logic Blocks (CLBs)2. In/Out Blocks (IOBs)3. Programmable Interconnection

- By fuse technology and be of OTP.- By antifusing or by type SRAM cells.

Depending on the manufacturer we can find differentsolutions. FPGAs currently available on the market, depending on the structure adopted by the logical blocksthat are defined, can be classified as belonging to fourmajor families shown, in the Figure 3.

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-

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-

-

---

---

-

Fig. 3. Block logic a) Symmetrical Array (XILINX), b) Sea ofGates (ORCA), c) Row Based (ACTEL) and d) HierarchicalPLD (ALTERA and XILINX).


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VOLUME 4, N° 4 2010

CLB IOB Interconection


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VOLUME 4, N° 4 2010

Fig. 5. CHIP Spartan of Xilinx Basic Elements.

Fig. 6. Block diagram in XSG of FLC.

a) b)

Fig. 7. Parameters of the Membership Functions. a) MFtrapezoidal, b) MF triangular.

Fig. 8. GA chromosome.

Table 1. Boundary parameters of the chromosome.

Fig. 9. Points of membership functions input and output.

Fig. 10. Range of parameters membership functions.

In Table 1, shows the boundary parameters of thechromosome.

Figure 9 shows the input of the FLC with fixed andvariable parameters. Each input and output has a size or8 bits.

The blue points are fixed, the red dots are for para-meter , the green dots are fixed and the yellow dotsare for parameter .

Figure 10 shows the range of parameters membershipfunctions.

a ba

2 1

1

( )

The GA is of multiobjective type [15], which meansthat to determine the best individual three evaluationsare performed:

a) Minimum overshoot

(3)

b) Minimum undershoot

(4)

c) Minimum output steady state error (sse)

(5)

The FLC linguistic terms were optimized with the GA,but the fuzzy rules are not changed. The process of the GAis shown in Figure 11.

To evaluate the ability of the GA, the FLC was simu-lated for speed control using a mathematical model of theplant in Matlab-Simulink [12], as shown in Figure 12.

Fig. 11. Optimization GA.

4. Test and Results the Novel GeneticOptimization of Membership Functionsfor FLC for Speed Regulate the Motor DC


Articles 57

VOLUME 4, N° 4 2010

Para

met

ers Input 1

0 < a < 128b = 128

128 < a < 255

2

1

1

Input Input 20 < a < 128

b = 128128 < a < 255

2

1

1

Output0 < a < 128

b = 128128 < a < 255

2

1

1


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The FLC has the inputs, error and change of error, and the output is the control signal . The

inputs are calculated as follows:

(6)

(7)

where is the sampling time.

The reference signal , is given by:

(8)

( ( ))( '( )) ( ( ))

( )= ( ) ( )

'( )= ( ) ( 1)

( )

e te t y t

e t r t y t

e t e t e t

t

r t

�

� �

Each input and output of the FIS has three linguisticterms. For the linguistic variable error and change oferror, the terms are {NB, Z, PB} in this case NB is NegativeBig, Z is Zero and PB is Positive Big. For the linguisticvariable control signal the linguistic terms are {BD, H,BI}, in this case BD is Big Decrement, H is Hold and BI isBig Increment.

A series of experiments was performed that are listedin Table 2.

In experiment No. 17 the best FLC was found becausethis has the lower error value. Below are the FIS charac-teristics for experiments 14 and 17.

Figure 13 shows how the GA modified the parametersof the membership functions for the input .e t( )

VOLUME 4, N° 4 2010

Fig. 12. Model.

Table 2. GA Parameters for different experiments.

r t =( ) 15 t � 00 t � 0

No.

123456789101112131415161718192021

Generations

2002002001002001501501002002002001001001001005050300300300200

Crossover(XOVSP)

0.80.80.80.80.80.80.80.80.80.70.7070.70.70.70.70.70.70.70.80.8

Selection(SUS)0.80.80.80.80.80.80.80.80.80.80.8080.80.80.80.80.80.80.80.80.8

Overshoot-Undershoot

0.40000.91040.40000.01480.41240.91040.1920

00.91040.91040.66000.91040.01480.41240.91040.0148

00.91040.02560.01480.9104

SSE

0.04250.10480.04250.01180.01980.10480.01100.08510.10480.10480.06370.10480.01180.01980.10480.01180.08140.10480.02050.01180.1048

Error

0.04137.7489e0.04130.01180.00210.00770.00270.05170.00770.00770.03457.75e0.0118

5.7457e7.75e0.0118

2.0788e7.75e2.538e0.01180.0077

-3

-3

-3

-3

-3

-3

-3

Time(sec)

1161.761412992.011800769.952523859.3038421030.261653896.357154689.695587754.005340924.325968839.401213810.448215711.466736804.630357671.710473709.538318822.235179723.025902960.829622941.8005891391.119402936.360153


Articles 59

VOLUME 4, N° 4 2010

Fig. 13. FIS for the experiment 14, input e(t).

Figure 14 shows the input modified by the GA.e t'( )

Fig. 14. FIS for the experiment 14, input e'(t).

Figure 15 shows the output of the FIS.y t( )

Fig. 15. Output FIS for the experiment 14.


Articles60

VOLUME 4, N° 4 2010

Figure 16 shows the control surface modified by the GA.

Fig. 16. Control Surface for experiment 14.

Figure 17 shows the output signal of the PD Incremental FLC for experiment 14.

Fig. 17. Velocity of the motor.

Figure 18 shows convergence the GA.

Fig. 18. GA convergence for experiment 14.


Articles 61

VOLUME 4, N° 4 2010

Figure 19 shows the best experiment for the input .e t( )

Fig. 19. Best FIS for the input e(t)).

'( )Figure 20 shows the input modified by the GA.e t

Fig. 20. Best FIS for the input e'(t).

( )Figure 21 shows the output of the FIS modified by the GA.y t

Fig. 21. Best FIS for the output (t).y


Articles62

VOLUME 4, N° 4 2010

Figure 22 shows the control surface modified by the GA.

Fig. 23. Velocity

Figure 24 shows convergence the GA for the best experiment.

Fig. 24. Shows the GA convergence error for experiment 17.

Fig. 22. Control Surface.

Figure 23 shows the output signal close loop of the FLC for experiment 17.


Articles 63

5. ConclusionsWe proposed a novel method for genetic optimization

of a fuzzy logic controller in FPGA for the regulation ofspeed of a DC motor, were the method optimizes threetriangular and trapezoidal membership functions for thetwo inputs and one output of the FLC.

The genetic algorithm optimizes only three of theeleven parameters of the membership functions, the algo-rithm proved to be very efficient with good results. Theobjective function of the GA considers three characteris-tics: overshoot, undershoot and steady state error, so thismakes it a multiobjective GA.

Each FIS was simulated in an Incremental PD FuzzyCon-troller for speed control of the DC motor. The best FLCwas obtained in 50 generations with 70% crossover and80% selection, with a result of zero of overshoot andunder-shoot steady state error of 2.0788e-3, in a time of723.025902 seconds with a speed of 15 rpm. Matlab-Simulink and Xilinx System Generator was used to performthe simulations.

-Tijuana Institute of Technology, Tijuana, Mexico. E-mail:[email protected].* Corresponding author

AUTHORSYazmin Maldonado, Oscar Castillo*, Patricia Melin

References[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[110]

[12]

[13]

[14]

Cirstea M.N., Khor J.G., McCormick M.,, Newnes, 2002.

Driankov D., Hellendorn H., Reinfrank M.,, Springer, 1996.

Goldberg D.E., , Optimiza-tion & Machine Learning, 1989.Jantzen J., , 1998,pp. 1-22.Klir G., Yuan B.,

, Prentice Hall, 1995.McNeilland D., Freiberger P.,

,Simon & Schuster, 1993.Tsoukalas L., Ohrig R.E.,

, WileyI-Interscience, 1997.Tommiska M., Vouri J.,”Implementation of geneticalgorithms with programmable logic devices”. In:

, 1996, pp. 71-78.Holland J. H.,

, Cambrige, MA: MIT Press, 1992.Golberg D.E.,

, Boston, MA: Addison-Wesley,1989.Grefenstette J.J., Gopal R., Rosmaita B.J., Van GuchtD., “Genetic Algorithms for the traveling salesman pro-blem”. In: , 1985,pp. 160-168.Web page of Matlab-Simulink, available inwww.mathworks.com, 2010.Web page of Xilinx system Generator and FPGAs,available in www.xilinx.com, 2010.Haupt Randy L., Haupt Sue E.,

Neural and fuzzylogic control of drives and power system

An Introduc-tion to Fuzzy Control

Genetic Algorithm in Search

Tunning of Fuzzy PID Controllers

Fuzzy Sets and Fuzzy Logic Theory andApplications

Fuzzy Logic: The Revolutio-nary Computer Technology that is Changing our World

Fuzzy and Neural Approaches inEngineering

Proc2 Nordic Workshop Genetic Algorithm

Adaptation in Natural and Artificial Sys-tems

Genetic Algorithms in Sear Optimizationand Machine Learning

Proc. 1 Int. Conf. Genetic Algorithms

Practial Genetic Algo-

nd

st

rithmsGenetic algorithms

Genetic Programming: on the Programming ofComputers by means of natural selection

Fuzzy Controller Design Theoryand Applications

IEEE NAFIPS Conference Proceedings

IEEE World Congress on computational Intel-ligence WCCI-2008

IEEE Internatio-nal Conference on Fuzzy Systems FUZZ-IEEE-2003

Procedimiento deDiseńo de Circuitos Digitales Mediante FPGAs

Diseńo y validación de la etapa de fuzzificacion para sistemas difusos enFPGAs

Soft Computinffor Hybrid Intelligent systems

The Type-2 Fuzzification Stage:Using Active Membership Functions, Evolutionary Designof Intelligent systems in Modeling, Simulation andControl

Validacion y Prueba de una Maquina de Inferencia Difusa Mediante XilinxSystem Generator

Methodology to Test and Validate a VHDL Inference Enginethrough the Xilinx System Generator, Soft Computinf forHybrid Intelligent Systems

Methodology to Test and Validate a VHDL Inference Engine of a Type-2 FIS, through the Xilinx System Generator,Evolutionary Design of Intelligent systems in Modeling,Simulation and Control

, Wiley, 2004.Man K.F., Tang K.S., Kwong S., ,Springer, 2000.Koza J.R.,

, 1992.Zadeh L.A., “Fuzzy Sets”, Information and Control 8,1965, pp. 338-353..Zdenko K., Stjepan B.,

, Taylor and Francis, 2006.Montiel O., Maldonado Y., Sepulveda R., Castillo O.,“Simple Tuned Fuzzy Controller Embedded into anFPGA”. In: , 2008,pp. 1-6.Montiel O., Maldonado Y., Sepulveda R., Castillo O.,“Development of an Embedded Simple Tuned Fuzzy Con-troller”. In:

, 2008, pp. 555-561.Velo F.J.M., Baturone L., Solano S.S., Barriga A., “RapidDesign of Fuzzy Systems with XFUZZY”,

, 2003,pp. 342-347.

[22] Buj Gelonch R.A., Sancho Francisco C.,, Univer-

sidad de Lleida, Escuela politécnica superior Escuelatécnica en informática de sistemas, 2007. (in Spanish)

[23] MaldonadoY., Montiel O., Sepulveda R., -

, ERA-08, 2008, pp. 1-7. (in Spanish)[24] Maldonado Y., Montiel O., Sepulveda R., Castillo O.,

“Design and simulation of the fuzzification Stagethrough the Xilinx System Generator”,

, Springer, 2008, pp.297-305.

[25] Montiel O., Sepulveda R., Maldonado Y., Castillo O.,Design and simulation of

, Springer, 2009, pp. 273-293.[26] Olivas J.A., Sepulveda R., Montiel O., -

, ERA-08, 2008, pp. 1-6. (in Spanish)[27] Olivas J.A., Sepulveda R., Montiel O., Castillo O., -

, Springer, 2008, pp. 325-331.[28] Sepulveda R., Oscar Montiel O., Olivas J., Castillo O.,

-

, Springer, 2009, pp. 295- 308.

[15]

[16]

[17]

[18]

[19]

[20]

[21]

VOLUME 4, N° 4 2010

Abstract:

1. Introduction

2. Related work

-

-

-

The international sourcing problem consists of selec-ting a subset of suppliers, with a finite production capacity, from an available set of potential suppliers locatedinternationally. In this paper we analyze the variantproposed in [1], which considers only a product in a single period and uncertainty on the demand and the exchange rate are modeled a set of scenarios. In theformulation of this problem it is assumed that the costsdepend on the economic conditions in the countries where the suppliers and the plants are located and that theproduction capacity of suppliers is finite. The robust formulation considers that a solution is feasible if and onlyif it is feasible in all the scenarios. The objective functionminimizes the expected value of the costs and penalizesthe solutions whose optimal cost in some scenario surpasses the expected value of the optimal costs in all thescenarios. Through this mechanism the associated risk isincorporated.

The rest of our paper is organized as follows: relatedwork, problem formulation, solution proposal and experi-mental results.

Now we summarize the most relevant works from theliterature about the plant location problem, because it is

This paper addresses the robust capacitated interna-tional sourcing problem (RoCIS), which consists of selec-ting a subset of suppliers with finite capacity, from anavailable set of potential suppliers internationally located.This problem was introduced by González-Velarde and Lag-una in [1], where they propose a deterministic solutionmethod based on tabu search memory strategies. The process consists of three steps: build an initial solution, createa neighborhood of promising solutions and perform a localsearch in the neighborhood. In this work we proposeimproving the construction of the initial solution, the construction of the neighborhood, the local search, and theintensification and diversification balance. Experimentalevidence shows that the improved tabu solution with diversification outperforms the best solutions reported for six ofthe instances considered, increases by 18% the number ofbest solutions found and reduces by 44% the deviation ofthe best solution found, respect to the best algorithmreported.

via

Keywords: RoCis, heuristic approach, optimization, initialsolution, tabu search, memory strategies.

-

--

-

-

-

closely related to the international sourcing problem.Jucker and Carlson solve a single product, single periodproblem, with price and demand uncertainty [2]. Hodderand Jucker present a deterministic single period, singleproduct model [3]. Hodder and Jucker optimally solvea single period, single product model, setting the plantsquantity [4]. Haug approaches the deterministic problemwith a single product and multiple periods with discountfactors [5]. Louveaux and Peters solve a scenario-basedproblem in which the capacity is a first stage decision[6]. Gutierrez and Kouvelis explore the generation of scenarios to model price uncertainty and solve a simple plantlocation problem [7]. Kouvelis and You propose an un-capacitated version robustness approach based on a minimax regret criterion [8] .

Now we describe the most relevant work about theinternational capacitated sourcing problem. The robustformulation of the international capacitated sourcingproblem was proposed by Gonzalez-Velarde and Laguna[1]. In this work they propose a solution method basedon the Benders paradigm, incorporating Tabu Search (TS)mechanisms. The process consists of building an initialsolution, creating a neighborhood of promising solutionsand performing a local search on the neighborhood. Asthe choice of the initial solution determines the efficiency of the process, this solution is constructed by applyinga heuristic that gives preference to suppliers with lowerfixed costs and greater production capacity.

González-Velarde and Martí propose a non-deterministic solution method based on GRASP, without incorporating the adaptive element, so the algorithm is classifiedas adaptive memory programming (AMP) type and pathrelinking is used to post processing the built solutions[9]. In the heuristic used to build a set of initial solutions, the shipping cost of each supplier to all plants isconsidered. The authors suggest that this way of incorporating the shipping cost seems too pessimistic.

In this work we propose to modify the TS based solution by improving the construction of the initial solution,the construction of the neighborhood, the local search,and the intensification and diversification balance.

-

--

-

--

-

-

-

AThe robust capacitated international sourcing pro-blem (RoCIS) consists of selecting a set of suppliers tosatisfy the demand for products at several plants locatedin different countries. The model deals with a single itemin a single period. The uncertainty in the demand and theexchange rates are modeled a set of scenarios. Themodel uses the following definitions:

3. Problem formulation

via

IMPROVING THE INTENSIFICATION AND DIVERSIFICATION BALANCEOF THE TABU SOLUTION FOR THE ROBUST CAPACITATED

INTERNATIONAL SOURCING PROBLEM (ROCIS)

Héctor Joaquín Fraire Huacuja, José Luis González-Velarde, Guadalupe Castilla Valdez


Articles64

Parameters

Variables

N nM mSf ic i

jb id se

sp s

x i js

y i

y y i m

s

: international plants set .: international suppliers set .

: scenarios set.: fixed cost associated with supplier .: total unit cost for delivering items from supplier

to plant .: capacity of supplier .: demand at plant j under scenario .: exchange rate at supplier's i location under

scenario .: occurrence probability of scenario .

: product shipment from supplier to plant underscenario .

: 1 if supplier is contracted and 0 otherwise.

Given a supplier selection , then theproblem becomes separable, and the following transpor-tation problem must be solved for each scenario :

Minimize(1)

subject to:

(2)

(3)

(4)

Then, the problem consists of minimizing:

(5)

where and .

The solution method reported in [1] is a heuristicsearch based on Benders decomposition paradigm. An ini-tial solution is constructed giving priority to the suppliersof smaller fixed cost and larger production capacity. Foreach supplier selection, the problem is decomposed intotransportation subproblems, one for each scenario. Theoptimal dual solution for each sub problem is used to finda promissory neighborhood and a local search in theneighborhood is carried out. The method uses severalshort term tabu memories, to monitor the suppliers usedin the visited solutions [3]. As the search goes, the bestfound solution is updated and continues until finishingthe exploration of the neighborhood. When the searchstops, a new search begins in the best found solutionneighborhood, the procedure continues during a certainnumber of iterations (50). Figure 1 shows the detailed al-gorithm for this solution method. As we can see the tabusolution, except for the diversification induced by theshort term memory, it does not include a long term diver-sification process.

{1, 2,..., }{1, 2,..., }

=[ ] =1,2,...

i

ij

i

js

is

s

ijs

i

i

4. Solution proposal

The reported solutions to RoCIS problem considers twostrategies to select the suppliers that must be incorpo-rated into an initial solution [1, 9]. The first one givespriority to the smaller fixed cost suppliers and greaterproduction capacity the second one incorporates theexpected value of the products shipment cost from theselected supplier to plants. The main limitation of thefirst strategy is that it does not consider the shipmentcost, and even though this factor is considered the secondone, the mechanism used is too pessimistic. In this workwe propose to modify the incorporation mechanism of theshipment cost,

.To describe this proposal, let the

shipment costs set from supplier to all the plants and BCia threshold cost defined on . Then, the set of plantstoward which the products shipment from the site of thesupplier is less expensive, can be defined as:

Now if and are the minimum and maximum ofthe shipment costs in , then can be modeled as:

To include in only the plants in , must be definedas:

The a value locates the initial solution on differentregions of the search space, and it can be used as a longterm diversification mechanism in the local search bydynamically changing its values.

To improve the quality of generated neighbors themechanism used to determine the relative cost of thethree types of movements that are applied to generate theneighborhood (insert, delete and suppliers exchange) ismodified. With the current definition, the movementsare selected based on their impact on the growth rate ofthe objective function, which could return in some casesan inappropriate choice. Currently is defined as:

where is the fixed cost of supplier , is

the expected dual price of supplier , is the occurrenceprobability of scenario and is the supplier dual pricein scenario .

In opposite would be more appropriate to select themovements

. Then

4.1. Improving the initial solution construction

4.2. Improving the neighborhood construction

all

to include only the plants towards which theproducts shipment from the site of the supplier is lessexpensive

based on the net increase of the objectivefunction generated when the movements are applied

C c j ni

C

i

c cC BC

G P

r

r

f i

i ps i

s

i ij

i

min max

i i

i i

i

i

i

s

is

={ | =1,2,... }

+

�

�


Articles 65

done. Table 1 shows the experimental results obtainedwith the improved tabu solution (ITS ), solving the in-stances with different values. The first column containsan identifier of the instance solved. The second one con-tains the best solution reported with AMP [9]. The follo-wing 8 columns contain the best solution found and thenumber of iterations required to find it with each algo-rithm used ( =0.2, 0.4, 0.6, and 0.8). The last columncontains the best global solution found by the algorithmsevaluated. For each algorithm, the best solution found isemphasized when this is the best overall solution. As wecan see on average approximately 12 iterations are need-ed for all ? values. As we can see the instances 25 and 29for =0.6 are which consume the largest number of itera-tions without reach the best known, and for =0.4 thebest known are achieved in few iterations. Then if we dis-card these instances the average iterations to achieve thebest solution is reduced as shown in Table 10. As we cansee the iterations required for =0.2 and 0.4 remainsaround 12, but for =0.6 it is reduced to 10. Therefore thesequence of values considered to use in the diversifi-cation process is the following:

This sequence takes advantage of the speed to reachthe greatest number of best solutions with = 0.6 andhelps to refine the results with the following values

=0.2, 0.4.

Supplier selection:

Hashing solution representation:

List of evaluated solutions:Tabu suppliers lists:

Building initial solution

1.1 Calculate

1.2 Build a list of suppliers in ascending order by

1.3 Build the solution , selecting suppliers in the sor-ted list until the sum of the capacities of the selec-ted suppliers is greater than .

1.4 Determine , solving the distribution subpro-blems generated for all scenarios.

1.5 Record the solution and its objective valuein the list of evaluated solutions

Repeat until reach 50 iterations2.1 Generate a promising solution neighborhood of2.1.1 Determine the expected value of shadow prices

linked to the constraint corresponding toeach supplier, in the solution of the sub pro-blems (for all the scenarios).

�

�

�

�

�

�

�

�

�

� � �

�

�

�

S

coded_sol H yinsertion, delete and swap

y

G

y

DF y

y F ycoded_sol H y

y

S

{ =0.6, =0.2, =0.4}

[ [ ]]

=

[ ]

[ ][ [ ]]

( )| |

0 ? 2

Data structure used:

Main algorithmStep 1:

Step 2:

i

is

r

b i

y'y''

y' y''y y

y = y' = y'' = , y =y = y' = y'' = , y = .

S' y'y''

S'' y'y''

y S'y'

y' S'S'' y''

y'' S'y

S

i

i

i i i i

i i i i

is redefined as:

where is the production capacity of supplier .

To improve the local search process is proposed toapply path re-linking on the two best global solutionsfound when each iteration ends, after the second itera-tion. The path re-linking strategy used is basically the de-scribed in [9]. The algorithm used to perform the processis shown in Figure 1.

prior best global solution found.actual best global solution found.

For each pair of solutions and :Determine the and solutions considering:

a. if and otherwiseb. if or otherwise

Determine the set of selected suppliers in butnot selected in

Determine the set of not selected suppliers inand selected in

Add to the solution the suppliers in inappropriated order to reach

Alternate between delete of a supplier of andadd a supplier of until reach the solution

Append to , one by one the suppliers of set inthe appropriate order to reach .

The evaluation of the ROCIS problem objective func-tion requires applying times the linear optimizer. Thisconstitutes the main source of computational cost of theTS method reported in [1]. To reduce this cost, the candi-date solutions evaluated and their objective values arerecorded. Each time that a candidate solution must beevaluated, the record is reviewed and if the candidate al-ready is recorded, the objective value is retrieved; other-wise, the candidate solution evaluation is performed andrecorded. This record can be used to determine the beha-vior of local search carried out in the neighborhood builtin the iteration. If the number of candidate solutions thatwere recorded is counted in each iteration, then we candetermine what neighborhood percentage has already be-en explored. High values of this percentage indicate thatthe local search is stangned and that a diversification pro-cess is required. When iteration ends, we can determine ifthe neighborhood percentage that has been explored, ex-ceeds a specified level (50% in our case). If this limit isreached, a new initial solution is built by assigning to the

parameter, a value that has not been used; otherwise,the iteration continues building a new neighborhood.

To determine the sequence of values used in thediversification process a preliminary experimentation was

,

Fig. 1. Path re-linking algorithm.

4.3. Improving the neighborhood local search

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

4.4. Incorporating a long term diversificationprocess

Data structures used:

� �

� �

� �

�

�

1 1 1 01 1 1 0

| |

�

�


fb

i

i

Articles66

2.1.2 Calculate the relative cost of the suppliers

2.1.3 For each of the possible insertions, deletions andswaps of suppliers that can be made from the solu-tion, validate the appropriate feasible configura-tion with respect to the maximum demand .

2.1.4 Build lists of candidates movements of insertion,deletion and swap, with

.The list of candidates for insertion containsthe suppliers with the 3 lowest values of .The list of candidates for deletion contains thesuppliers with the 3 highest values of .The list of candidates for swap contains the

suppliers with the lowest values of

corre-sponding to the swap between supplierby supplier in configuration .

2.2 Do local search2.2.1 For each configuration generated from the

movements of the candidate lists of insertion,deletion and swapping:

2.2.1.1 The suppliers involved in the movement usedto generate the configuration are: appen-ded to the insertion tabu list (if the move-ment was for deletion), or removed (if themovement was to insertion). This two tabulists are used too when a swap movement isapplied, cnsidering that a swap movementrequires a deletion and an insertion. Thenumber of iterations during which a supplierinvolved in a movement is considered tabuare: for insertions and eliminations and

for swaps.

2.2.1.2 If the solution is already saved in the listof evaluated solutions , itsobjective value is retrieved, otherwise

is calculated and appended to thelist.

2.2.1.3 Update the best solution found .2.2.2

Supplier selection:

Hashing solution representation:

List of evaluated solutions:Tabu suppliers lists:

( .)

[ [ ]][ ]

[ ]

[ [ ]]

r

D

r

r

r -

ri j y

y'

y'

y'coded_sol H y

F y'F y'

yy = y

coded_sol H yinsertion, delete and swap

i

i

i

j

i

best

best

the movements identifiedin the previous step that are not stored in the tabulist for each type of movement

Fig. 2. Tabu solution algorithm TS [1].

�

�

�

Data structures used:

As part of the diversification mechanism the followingvariables and constants are defined:

The counter of candidate solutions generated inthe current neighborhood already registered in the ha-shing list.

The number of candidate solutions in the currentneighborhood:

The percentage of the current neighborhood had al-ready been reviewed in previous iterations (stagnationlevel observed):

InitialSolution( )

Calculate

Build a suppliers list in ascending sorted by

where and

where

Build the solution , selecting suppliers in the sor-ted list until the sum of the capacities of the selected sup-pliers is greater than .

Determinate , solving the transportation subproblems generated in all scenarios.

Record the solution and its objective valuein the list of evaluated solution

Return the actual solution .

Repeat until 50 iterations

3.1 Generate a promising solution neighborhood of2.1.1 Determine the expected value of shadow prices

linked to the constraint corresponding toeach supplier, in the solution of the 27 sub pro-blems (for all the scenarios).

3.1.2 Calculate the suppliers relative cost

3.1.3 For each of the possible insertions, deletions andswaps of suppliers that can be made from the solu-tion, validate the feasibility of configuration with

RC:

Function

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

Step 1:Step 2:Step 3:

NCS = 3 + 3+

[ ]

[ ][ [ ]]

= 0= l( =0.6)

( )

( .)

SL = RC / NCS

y

DF y

y F ycoded_sol H y

y

changey SoluciónInicia

y

r

�

�

�

Main algorithm

is

i


Articles 67

AMP33178.6345844181.4821039558.8243747120.4763941515.9339241285.5738842015.0458555627.0748346055.9867257188.4164760692.5887555603.7985867389.8032965420.8066778184.0241538094.8666934109.3105934127.4802240558.7981632210.9675941551.6503938833.6767544391.6369341831.9458553709.1886361377.2609169464.0578775482.5976661818.8914068193.73131

ITS 0.433178.6345844181.4821039558.8243747120.4763941515.9339241285.5738842015.0458555627.0748346055.9867257188.4164760692.5887555617.1635668158.7615265427.0081078184.0241537809.0095534109.3105933814.0991040558.7981631496.8480441527.7708738833.6767544391.6369341831.9458553709.1886361377.2609169496.3024775482.5976661818.8914068193.72023

ITS 0.633178.6345844181.4821039558.8243747120.4763941515.9339241285.5738842015.0458555627.0748346055.9867257188.4164760692.5887555603.7985868158.7615265420.8066778184.0241537809.0095534109.3105933814.0991040558.7981631496.8480441741.1555138833.6767544391.6369341831.9458554180.9660561377.2609169464.0465475952.1136561963.3742668193.72023

ITS 0.233178.6345844181.4821039558.8243747120.4763941515.9339241285.5738842015.0458555627.0748346055.9867257188.4164760692.5887555603.7985867389.8032965595.8752378184.0241537809.0095534109.3105933814.0991040558.7981631496.8480441741.1555138833.6767544391.6369341831.9458553709.1886361377.2609169541.1768175482.5976662170.3268968073.37865

ITS 0.833178.6345844181.4821039558.8243747120.4763941515.9339241285.5738842015.0458555627.0748346055.9867257188.4164760692.5887555617.1635668158.7615265420.8066778184.0241537820.6501534109.3105933814.0991040570.8448731496.8480441741.1555138833.6767544391.6369341831.9458553709.1886361377.2609169464.0465475482.5976661851.6094068292.71756

Best33178.6345844181.4821039558.8243747120.4763941515.9339241285.5738842015.0458555627.0748346055.9867257188.4164760692.5887555603.7985867389.8032965420.8066778184.0241537809.0095534109.3105933814.0991040558.7981631496.8480441527.7708738833.6767544391.6369341831.9458553709.1886361377.2609169464.0465475482.5976661818.8914068073.37865

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10109781712952811913247121291112725126810920524

99791057111029109102111991197111364382644418

81061613131179320237103611912301210101128101945203017

respect to the maximum demand .3.1.4 Build lists of candidate movement for insertion,

deletion and swap, with .The list of candidates for insertion containsthe suppliers with the 3 lowest values of .The list of candidates for deletion contains thesuppliers with the 3 highest values of .The list of candidates for swap contains the

suppliers with the lowest values of

- corresponding to the swap between supplierby supplier in configuration

3.2 Local search process3.2.1 For each configuration generated from the mo-

vements of the candidate lists of insertion, dele-tion and swapping:

3.2.1.1 The suppliers involved in the movementused to generate the configuration are:appended to the insertion tabu list (if themovement was for deletion), or removed (ifthe movement was to insertion). This twotabu lists are used too when a swap move-ment is applied, cnsidering that a swap mo-vement requires a deletion and an inser-tion. The number of iterations during whicha supplier involved in a movement is consi-dered tabu are: for insertions and elimi-

D

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y'

aspiration criteria�

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nations and for swaps.

3.2.1.2 If the solution is already saved in the listof evaluated solutions, its objective value

is retrieved and the repeated candi-date solutions counter RC is incremented,otherwise is calculated and appendedto the list.

3.2.1.3 Update the best solution found .3.2.2 Path relinking process

3.2.2.1 From the second iteration, update the twobest solutions found.

3.2.2.2 Apply path relinking to the two best solu-tions found and update

3.2.3 Diversification process3.2.3.1 Calculate the stagnation level3.2.3.2 If

then

If then

If then

Else

y'

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SL=RS/NCSSL

change=changechange

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=InitialSolution( =0.2)( =2)

=InitialSolution( =0.4)

best

best

best

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Fig. 3. Improved tabu solution with diversification ITSDalgorithm.


Table 1. Performance of the improved tabu solution ITS (with = 0.2, 0.4, 0.6, 0.8 and 50 iterations).�

Articles68


As it is showed in Figure 3, the InitialSolution( ) fun-ction is used to diversify the search and is initially in-voked with . When the observed stagnation level rea-ches 50%, after a complete exploration of the currentneighborhood, the InitialSolution( ) function is invokedwith . The search continues and when the stagnationlevel reaches 50% again, the InitialSolution( ) functionis called with . Then the search continues until finish,without changing the value.

Figure 3 shows the detailed proposed tabu solutionalgorithm, which incorporates the improvements in theconstruction of the initial solutions, in the constructionof neighborhoods, in the local search, and the long termdiversification mechanism.

The experiments were done in a computer Dell Opti-plex 160L with a Pentium IV processor to 2.4 GHZ and 1 GBram. The source code was compiled using Visual C 6.0 andthe operating system Windows XP. For the solution of thetransportation sub problems LINDO API 2.0 was used. Toevaluate the performance of the algorithms, the largerinstances reported in [9] were used. The instances weregenerated with 20 plants, 40 suppliers and 27 scenarios,and constitute a representative sample of instances withthe same size and different hardness degrees. As the opti-mal solutions for these instances are not known, the re-sults obtained in this work are compared with the best so-lutions reported in [9]. To evaluate the impact of the pro-posed improvements on the TS performance, four types ofexperiments were carried out.

In the first one the proposed improvements for theinitial construction, the construction of the neighbor-hood and local search were evaluated. Table 1 shows theresults obtained with the improved tabu solution (ITS ),for different values. The table shows that the improved TSfound better solutions than those reported for instances16, 18, 20, 21, 27 and 30. As we can observe the bestglobal solutions found by AMP are also found by ITS usingone or more of the values. However there is not a singlevalue which allows finding the best global solution for allinstances. Experimental evidence confirms that the valueoperates as a diversification mechanism on the searchprocess.

Table 2 shows a summary of the experimental results,including: the average cost of the found solutions, thenumber of overall best solutions found, the error rate overthe average cost of best solution and the average timeused to solve each instance (in CPU seconds).

In other hand, in Table 1 we can observe that 4 ITS al-gorithms obtains the best known solutions for 19 instan-ces, and similarly 3 ITS algorithms for 3 instances, 2 ITSalgorithms for 4 instances and 1 ITS algorithm for 4 ins-tances. Then if four groups of instances are considered: ,

, and , where the group contains all the instancesfor which ITS algorithms obtains the best known solu-tions. We could consider that for , the instances in

are easiest than the instances in . Then the questionis a structural and landscape analysis of the instancescan help us to explain the relative hardness observed?

In the second experiment the structural analysis ofthe instances was done. For all instances the sparsity, the

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II I I I

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variation coefficient and the skewness of the instanceparameters (shipment cost matrix, fixed cost vector, ca-pacity supplier vector, plants demand matrix and currencyrate matrix) were calculated. The sparsity measures thepercentage of parameter structure elements that are equalto zero; the main interest in this measure is that accor-ding to Mitchell and Borchers, it has a strong influence onalgorithm behavior [11]. The (VC) isdefined as where is the standard deviation andthe mean of the structure elements. VC gives an estimateof the variability of the structure elements, independentof their size. The is the third moment of themean normalized by the standard deviation; it gives anindication of the degree of asymmetry of the structureelements. In the experiment all the instances were consi-dered grouped in , , and . Then the sparsity, thevariation coefficient and skewness were calculated for thefive components of each instance: shipment cost matrix,fixed cost vector, capacity supplier vector, plants demandmatrix and currency rate matrix. For all the instances andcomponents the observed sparsity percentage was zero.Table 3 contains the obtained results for the variation co-efficient and Table 4 the results for the skewness. As wecan observe the four instances groups shows a similarstructure, because the differences between the values ofthe variation coefficient and of the skewness are minimal.In the third experiment a ruggedness analysis of the land-scape was done. The central idea of the landscape analysisin combinatorial optimization is to represent the spacesearched by an algorithm as a landscape formed by all fea-sible solutions and the objective value assigned to eachsolution [12]. The information generated with the land-scape analysis is used to gain knowledge about: thesearch space characteristics and their relation with thebehavior of local search or metaheuristic algorithms[13],[14], problem or problem instance hardness [15],[16], or useful parameterizations of local searchalgorithms [17]. A search landscape is considered ruggedif there is a low correlation between neighboring points.To measure this correlation a of length , isperformed in the search landscape to interpret theresulting series of points as a timeseries. The autocorrelation of the points in the seriesthat are separated by steps is defined as:

where and are the variance and the mean of thepoints in the series. Now the

is defined as:

where . Then the lower is the value of , themore rugged is the landscape [18].

Previously to the determination of the search spacecorrelation length values for the instances in the con-sidered groups, we must determine the length of the ran-dom walk to be applied. For this purpose were calculatedfive times the average of the values of all the instanceswith a random walk length given. The obtained results,

variation coefficient

skewness

random walk

search landscape correlationlength

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VOLUME 4, N° 4 2010

Articles 69


Val.# Bests

Dev.CPU secs

Shipment costMin

MedianMaxMean

Search landscape correlationlength ( value)l

MinMedian

MaxMean

Walk

12345

Supplier capacityMin

MedianMaxMean

Fixed costMin

MedianMaxMean

DemandMin

MedianMaxMean

Exchange rateMin

MedianMaxMean

I0.450.480.480.47

1

I0.170.200.220.19

1

l average(Length=1000)

0.250.260.280.280.25

l average(Length=50000)

0.190.180.200.190.20

I0.100.120.120.12

1

I0.100.120.120.12

1

I0.150.160.160.16

1

I0.100.100.100.10

1

I0.460.480.490.48

2

I0.160.180.210.18

2

I0.110.110.120.11

2

I0.110.110.120.11

2

I0.150.160.160.16

2

I0.100.100.100.10

2

I0.460.470.490.47

3

I0.130.160.170.15

3

I0.110.120.120.12

3

I0.110.120.120.12

3

I0.160.160.160.16

3

I0.100.100.100.10

3

I0.450.470.500.47

4

I0.140.190.230.19

4

I0.100.120.130.11

4

I0.100.120.130.11

4

I0.150.160.170.16

4

I0.100.100.100.10

4

AMP50359.15105

240.10%218.23

TS51730.25

12.93%381.25

ITS 0.250337.79759

260.05%374.22

ITS 0.450341.93472

250.06%392.92

ITS 0.650383.51267

240.14%371.75

ITS 0.850352.94571

230.08%368.97

Best50310.56363

300%

Table 2. Comparative summary of the performance of the improved tabu solution ITS with 50 iterations.

Table 3. Structural information of the instancesgroups , , and (variation coefficient).I I I I1 2 3 4

Table 5. Average l value obtained in five random walkswith two lengths: 1000 and 50000 steps.

Table 6. Minimum, median, maximum and mean of the searchlandscape correlation length (l value) obtained with a randomwalk of 50000 steps, for the groups , , and .I I I I1 2 3 4

Graph 1. Average l value obtained in five random walkswith two lengths: 1000 and 50000 steps.

Table 3. Structural information of the instancesgroups , , and (variation coefficient).I I I I1 2 3 4

Shipment costMin

MedianMaxMean

Supplier capacityMin

MedianMaxMean

Fixed costMin

MedianMaxMean

DemandMin

MedianMaxMean

Exchange rateMin

MedianMaxMean

I0.080.170.230.16

1

I-0.10-0.030.500.09

1

I-0.10-0.030.500.09

1

I-0.05-0.040.03-0.02

1

I-0.030.000.090.01

1

I0.130.170.250.18

2

I0.000.130.490.19

2

I0.000.130.490.19

2

I-0.10-0.010.120.00

2

I-0.08-0.010.05-0.01

2

I0.170.250.380.27

3

I-0.300.000.22-0.03

3

I-0.300.000.22-0.03

3

I-0.060.020.050.00

3

I0.050.060.070.06

3

I-0.030.190.350.17

4

I-0.56-0.050.64-0.01

4

I-0.560.080.640.09

4

I-0.12-0.030.10-0.01

4

I-0.060.020.060.01

4

Table 4. Structural information of the instancesgroups , , and (skewness).I I I I1 2 3 4

Articles70


with random walk lengths of 1000 and 50000 steps, areshowed in Table 5 and Graph 1. As we can observe, with1000 steps the average of the values varies from 0.25 to0.28 and for 50000 steps varies from 0.18 to 0.20. Giventhe high resource consumption required to solve theROCIS instances, we consider that with 50000 steps theaverage of the values shows an appropriated precisionlevel and stability. Now we calculate the values for theinstances in each group using a random walk with 50000steps. Table 6 shows the minimum, median, maximum andthe mean of the average values for each group ( , ,and ). As we can observe that do not exist a significantdifference respect to the landscape ruggedness generatedfor the random walk with the instances of the differentgroups. All the average values are very similar and closerto zero. The random walk algorithm seems perceive thatall the instances have a high hardness level regardless ofthe group that they belong. Then it seems more appro-

l

ll

l I I II

l

1 2 3

4

priate to incorporate in the tabu solution a long termdiversification process to avoid to get stuck in the localoptimums.

In the last experiment the performance of the impro-ved tabu solution with diversification (ITSD) was evalua-ted. As we can see in the section 4.4. (Incorporatinga diversification process), the sequence of a values usedin the diversification process is the following:

The ITSD algorithm starts with =0.6 and the firsttime that stagnation is detected, is changed to 0.2 and inthe second one switches to 0.4. The search continueswith the last one value, until reaching the stoppingcondition

Table 7 shows the comparative performance of theITSD algorithm with respect to ITS algorithm (for =0.2,

S { =0.6, =0.2, =0.4}� � �

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VOLUME 4, N° 4 2010

AMP33178.6345844181.4821039558.8243747120.4763941515.9339241285.5738842015.0458555627.0748346055.9867257188.4164760692.5887555603.7985867389.8032965420.8066778184.0241538094.8666934109.3105934127.4802240558.7981632210.9675941551.6503938833.6767544391.6369341831.9458553709.1886361377.2609169464.0578775482.5976661818.8914068193.73131

ITS 0.433178.6345844181.4821039558.8243747120.4763941515.9339241285.5738842015.0458555627.0748346055.9867257188.4164760692.5887555617.1635668158.7615265427.0081078184.0241537809.0095534109.3105933814.0991040558.7981631496.8480441527.7708738833.6767544391.6369341831.9458553709.1886361377.2609169496.3024775482.5976661818.8914068193.72023

ITS 0.633178.6345844181.4821039558.8243747120.4763941515.9339241285.5738842015.0458555627.0748346055.9867257188.4164760692.5887555603.7985868158.7615265420.8066778184.0241537809.0095534109.3105933814.0991040558.7981631496.8480441741.1555138833.6767544391.6369341831.9458554180.9660561377.2609169464.0465475952.1136561963.3742668193.72023

ITS 0.233178.6345844181.4821039558.8243747120.4763941515.9339241285.5738842015.0458555627.0748346055.9867257188.4164760692.5887555603.7985867389.8032965595.8752378184.0241537809.0095534109.3105933814.0991040558.7981631496.8480441741.1555138833.6767544391.6369341831.9458553709.1886361377.2609169541.1768175482.5976662170.3268968073.37865

ITSD33178.6345844181.4821039558.8243747120.4763941515.9339241285.5738842015.0458555627.0748346055.9867257188.4164760692.5887555603.7985867433.6047265420.8066778184.0241537809.0095534109.3105933814.0991040558.7981631496.8480441527.7708738833.6767544391.6369341831.9458553709.1886361377.2609169464.0465475482.5976661818.8914068073.37865

Best33178.6345844181.4821039558.8243747120.4763941515.9339241285.5738842015.0458555627.0748346055.9867257188.4164760692.5887555603.7985867389.8032965420.8066778184.0241537809.0095534109.3105933814.0991040558.7981631496.8480441527.7708738833.6767544391.6369341831.9458553709.1886361377.2609169464.0465475482.5976661818.8914068073.37865

123456789101112131415161718192021222324252627282930

12121210122071063261114962210109111187187112752811

10109781712952811913247121291112725126810920524

99791057111029109102111991197111364382644418

99791057111029101910181199119301113638849154024

Table 7. Performance of the improved tabu solution with diversification ITSD and 50 iterations.

Val.# Bests

Dev.CPU secs

AMP50359.15105

240.10%218.23

TS51730.25

12.93%381.25

ITS 0.250337.79759

260.05%374.22

ITS 0.450341.93472

250.06%392.92

ITS 0.650383.51267

240.14%371.75

ITS 0.850312.02403

290.003%386.94

Best50310.56363

300%

Table 8. Comparative summary of the performance of the improved tabu solution with diversification ITSD and 50 iterations.

Articles 71

0.4 and 0.6) and AMP algorithm. As we can see, thesolution with diversification is able to find 29 of the 30global best solutions, outperforming all the algorithmsevaluated. Table 8 shows a summary of the experimentresults. Tables 2 and 8 shows that with 50 iterations ITS(with = 0.2 and 0.4) and ITSD are better in quality thanAMP, but the last one is better than ITS and ITSD inefficiency.

To reduce the resources consumption of ITS and ITSD,the number of iterations was reduced to 30. Table 9 showsthe obtained results and we can observe that now ITSDoutperfoms in quality and efficiency to ITS (for =0.2)and to AMP.

This paper approaches the robust capacitated interna-tional sourcing problem (RoCIS) which consists of selec-ting a subset of suppliers with finite capacity, from anavailable set of potential suppliers internationally loca-ted. The tabu solution proposed in [1] consists of threephases: build an initial solution, create a neighborhood ofpromising solutions and perform an extensive search inthe neighborhood. In this work the construction of theinitial solution, the construction of the neighborhood,and the local search were improved. Also the intensifi-cation and diversification balance of the tabu solutionwas improved, incorporating a long term diversificationprocess. Experimental evidence shows that the improvedtabu solution with diversification outperforms the bestsolutions reported for six of the instances considered,increases 18% the number of best solutions found andreduces 44% the deviation from the best solution found,respect to the best algorithm solution reported.

Future work includes improving the efficiency of theproposed solution, incorporating different diversificationmechanisms and stopping conditions based on the stag-nation detection.

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Table 9. Comparative summary of the performance of theimproved tabu solution with diversification ITSD and 30iterations.

Table 10. Average iterations needed for the improved tabuto reach the best solution without instances 25 and 29.

6. Conclusions and future work

ACKNOWLEDGMENTSAuthors thank the support received from Tecnológico de Mon-terrey, Consejo Nacional de Ciencia y Tecnología (CONACYT) andConsejo Tamulipeco de Ciencia y Tecnología (COTACYT) throughprojects CAT128, CONACYT-67032 and TAMPS-2007-C15-


106096 respectively, for the research reported in this paper.

[1]

AUTHORSHéctor Joaquín Fraire Huacuja, Guadalupe CastillaValdez

José Luis González-Velarde

References

- Instituto Tecnológico de Ciudad Madero. 1° deMayo y Sor Juana I. de la Cruz S/N, Ciudad Madero Tama-ulipas, México CP. 89440.

- Centro de Calidad y Manu-factura, Tecnológico de Monterrey, Monterrey NuevoLeón, México.* Corresponding author

González-Velarde J.L., Laguna M., “A Benders-basedheuristic for the robust capacitated international sour-cing problem. IIE Transactions, vol. 36, 2004, pp. 1125-1133.

[2] Jucker J.V., Carlson R.C., “The Simple Plant-LocationProblem under Uncertainty. , vol.24, no. 6, 1976, pp. 1045-1055.

[3] Hodder J.E., Jucker J.V., “Plant Location Modeling forthe Multinational Firm”. In:

, Honolulu, Decem-ber 1982, pp. 248-258.

[4] Hodder J.E., Jucker J.V., “A Simple Plant-Location Mo-del for Quantity-Setting Firms subject to Price Uncer-tainty”, , vol.21, 1985.

[5] Haug P.A., “Multiple-Period, Mixed-Integer-Program-ming Model for Multinational Facility Location”,

, vol. 11, no.3, 1985, pp. 83-96.[6] Louveaux F.V., Peters D., “A dual-based procedure for

stochastic facility location”, , vol.40, no. 3, 1992, pp. 564-573.

[7] Gutiérrez G.J., Kouvelis P., “A Robustness Approach toInternational Sourcing”, ,vol. 59, 1995, pp. 165-193.

[8] Kouvelis P., Yu G.,, Dordrecht: Kluwer Academic Publishers,

1997.[9] González-Velarde J.L., Martí R., “Adaptive Memory Pro-

gramming for the Robust Capacitated InternationalSourcing Problem”, ,vol. 35, no. 3, 2008, pp. 797-806.

[10] Glover F., Laguna M., , Kluwer AcademicPublishers, 1997.

[11] Mitchell J.E., Borchers B., “Solving linear ordering pro-blems with a combined interior point/simplex cuttingplane algorithm”. In: H. L. Frenk , editor,

, Kluwer Academic Publishers,Dordrecht, The Netherlands, 2000, pp. 349-366.

[12] Merz P., Freisleben B., “Fitness landscapes and memeticalgorithm design”. In: D. Corne, M. Dorigo, and F. Glo-ver, editors, , McGraw-Hill,London, 1999, pp. 245-260.

[13] Boese K. D., .PhD thesis, University of California, Computer ScienceDepartment, Los Angeles, CA, USA, 1996.

[14] Stutzle T., Hoos H.H., MAX-MIN Ant System.

Operations Research

Proceedings of the Academyof International Business Conference on the Asia-PacificDimension of International Business

European Journal of Operational Research

Jour-nal of Management

Operations Research

Annals of Operations Research

Robust Discrete Optimization and itsApplications

Computers and Operations Research

Tabu Search

et al. HighPerformance Optimization

New Ideas in Optimization

Models for Iterative Global Optimization

Future

VOLUME 4, N° 4 2010

Val.# Bests

Dev.CPU secs

Average Iterationsuntil the best

reached

AMP50,359.15105

220.10%218.23

ITS 0.212.10714

ITS 0.250,344.08684

250.066%235.76

ITS 0.412.42857

ITSD50,310.56363

260.056%218.20

ITS 0.610.00000

Articles72


Generation Computer Systems

Discrete AppliedMathematics

Physics Letters A

Theoretical Com-puter Science

BiologicalCybernetics

, vol. 16(8), 2000, pp.889-914.

[15] AngelE., Zissimopoulos V., “On the classification of NP-complete problems in terms of their correlation coef-ficient”. , no. 99, 2000,pp. 261-277.

[16] Stadler P.F., Schnabl W., “The landscape of the travel-ling salesman problem”, , 161, 1992,pp. 337-344.

[17] Angel E., Zissimopoulos V., “Autocorrelation coefficientfor the graph bipartitioning problem”,

, no. 191 1998, pp. 229-243.[18] Weinberger E. D., “Correlated and uncorrelated fitness

landscapes and how to tell the difference”,, no. 63, 1990, pp. 325-336.

VOLUME 4, N° 4 2010

Articles 73

Abstract:

1. IntroductionRobots are being more commonly used in many areas

of research and a reason for this is that they are becomingmore accessible economically for researchers. In thispaper we consider the optimization of a fuzzy controller;that gives the ability of reaction to the robot. This may betoo general, so let's limit what in this paper will be des-cribed as ability of reaction - this is applied in the naviga-tion concept, so what this means is that when the robotis moving, and at some point of its journey it encountersan unexpected obstacle, it will react to this stimulationavoiding and continuing on its path. The trajectory andpath following are considered independent parts and arenot consider on this paper [19].

There are many traditional techniques available touse in control, such as PD, PID and many more, but wetook a different approach in the Control of the robot,using an area of soft computing which is fuzzy logic thatwas introduced by Zadeh [1]. Later this idea was appliedin the area of control by Mamdami [2], where the conceptof FLC (Fuzzy Logic Controller) originated. It is also im-portant to mention that this is not the only area were thefuzzy concepts are applied but it is where the most workhas been done, and were many people have contributedimportant ideas and methods like Takagi and Sugeno [2].

There are many recent papers on controlling mobilerobots with intelligent techniques, in particular with fuz-zy logic and genetic algorithms [3], [4], [5], [6], [7].However, in this paper the proposed approach is to use anevolutionary algorithm to optimize the fuzzy logic reac-tive controller of a mobile robot. There are also severalworks on using fuzzy logic for tracking control and navi-gation of mobile robots [8], [9], [10], [11], [12], [13],[14], [15], [16], [19] ,[20].

This paper is organized as follows: in section 2 wedescribe the mobile robot used in these experiments, sec-tion 3 describes the development of the evolutionarymethod. Section 4 shows the simulation results. Finally,section 5 presents the Conclusions.

This paper describes an evolutionary algorithm applica-tion for the optimization of a reactive fuzzy controller ap-plied to mobile robot navigation. The evolutionary algo-rithm optimizes the fuzzy inference system and the posi-tion and number of the sensors on the robot, while trying touse the less power possible.

Keywords: fuzzy control, genetic optimization, geneticfuzzy systems, robotic systems.

2. Mobile RobotThe robot is based on the description for mobile ro-

bots presented in [21] and assumes a wheeled mobile ro-bot consisting of one or two conventional, steered, un-actuated and not-sensed wheels and two conventional,actuated, and sensed wheels (conventional wheel chairmodel). This type of chassis provides two DOF (degrees offreedom) locomotion by two actuated conventional non-steered wheels and one or two un-actuated steeredwheels. The Robot has two degrees of freedom (DOFs):y-translation and either x-translation or z-rotation [21].Fig. 1 shows the robots configuration, it will have 2 inde-pendent motors located on each side of the robot and onecastor wheel for support located at the form of the robot.

The kinematic equations of the mobile robot are asfollows:

Equation 1 is the sensed forward velocity solution [21]

(1)

Equation 2 is the Actuated Inverse Velocity Solution [21]

(2)

Where under the Metric system we have the following:

Fig. 1. Kinematic coordinate system assignments [21].

V V

Rl l

Bx By

Bz

W W

a b

, - Translational velocities [m/s],- Robot z-rotational velocity [rad/s],, - Wheel rotational velocities [rad/s],

- Actuated wheel radius [m],, - Distances of wheels from robot's axes [m].

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OPTIMIZATION OF A REACTIVE FUZZY LOGIC CONTROLLERFOR A MOBILE ROBOT USING EVOLUTIONARY ALGORITHMS

Abraham Meléndez, Oscar Castillo, Arnulfo Alanis


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Articles74

Fig. 3. Fitness FIS.

Fig. 4. Chromosome Architecture.

Fig. 5. Sample trajectories of the proposed approach.

The chromosome architecture, is shown in Fig. 4, whe-re we have encoded the membership functions type andparameters, we have set a maximum number of 5 member-ship functions for each of the outputs and input and out-put variables.

All the results obtain will get persisted on a Data Base,were we will store each step on the genetic cycle, keepingtrack of the genealogy of each chromosome, and with thiswe can examine each of the top individuals and can backtrack the behavior of the genetic algorithm.

We have worked on the reactive control for a mobilerobot before, where we use a particular maze problem totest the effectiveness of each of the reactive controls,and we did not use any optimization strategy to fine tunethe controllers as it was a manually process, and becauseof that experience we decided to apply GA to this pro-blem. In Fig. 5 and Table I one can see the results weobtained in our prior experiments for fuzzy systems of 27rules and 10 rules, respectively.

4. Simulation Results

3. Evolutionary Method DescriptionIn this section we will describe the Genetic Algorithm

applied to the problem of finding the best fuzzy logic re-active controller for a mobile robot. The genetic algorithmoptimizes the structure of the fuzzy system for control,which means tuning the membership functions and opti-mizing the number of fuzzy rules.

The purpose of using a evolutionary method, is to ob-tained the best reactive control possible, for the robot,but also taking into consideration other desirable charac-teristics on the robot that we want to improve making thisa multi objective [17] problem, for this we will take ad-vantage of the HGA (Hierarchy Genetic Algorithm) intrin-sic characteristic to solve multi objective problems, nowlet us state the main goal of our HGA.

The main goal is to optimize the Reactive Control ta-ken in to consideration the following:

Fine tune the Fuzzy MembershipsOptimize the FIS if then fuzzy rulesThe mobile robot Power Usage

In Fig. 2, we show the global cycle process of the GA,under the Evaluation of the each individual, is where weare going, to measure the goodness of each of the FIS(Fuzzy Inference System) represent by each Individualchromosome, in our test area, that will take place ina unknown environment (Maze [18]) to the robot wherethe robot's objective will be find the exit, avoiding hittingthe walls and any other obstacle present.

Our criteria to measure the Fuzzy Inference System(FIS) global performance will take into consideration thefollowing:

Cover Distance,Time used to cover distance,Battery life.

All of these variables are the inputs of the EvaluationFIS that we will use to obtain the fitness value of eachchromosome. In Figure 3 the structure of the fuzzy infe-rence system is illustrated.

The FIS that we optimized is a Mamdani type fuzzysystem, consisting of 3 inputs that are the distances ob-tain by the robots sensors describe on section 2, and2 outputs that control de velocity of the servo motorson the robot, all this information is encoded on eachchromosome.

�

�

�

�

�

�

Fig. 2. Genetic Algorithm process.


Cover Distance (3)

Running Time (3)

Fitness(mamdani)27 rules

Fitness (5)

Power Level (3)

Articles 75

5. ConclusionsPreliminary results show promising data and as ex-

pect the HGA improves the overall performance of thecontroller for the mobile robot, and improves the resultsobtained previously. The best reactive controller obtai-ned with the HGA with the same maze problem outper-forms the best reactive controller obtained manually,which supports the idea that an evolutionary algorithmoptimizes the structure and parameters of the fuzzy logiccontroller.

-Graduate Division, Tijuana Institute of Technology,Tijuana, BC 22379, Mexico. Email: [email protected]* Corresponding author

ACKNOWLEDGMENTS

AUTHORSAbraham Meléndez, Oscar Castillo*, Arnulfo Alanis

References

We would like to express our gratitude to the CONACYT, andTijuana Institute of Technology for the facilities and resourcesgranted for the development of this research.

[1] Aceves A., Aguilar J., “A Simplified Version of Mam-dani's Fuzzy Controller The Natural Logic Controller”,

, vol. 14, no. 1, 2006,p. 1630.

[2] Astudillo L., Castillo O., Aguilar L.T. “Intelligent Con-trol of an Autonomous Mobile Robot Using Type-2 FuzzyLogic”, vol. 14, no. 1,pp. 37-48.

[3] Astudillo L., Castillo O., Aguilar L., “Control Difuso deRobots Autónomos Móviles en Ambientes Inciertos us-ando Lógica Difusa”, Tesis, División de Estudios y Pos-grados e Investigación, ITT, México, October 2006.

IEEE Transactions on Fuzzy Systems

Journal of Nonlinear Studies,

Table 1. Reactive Control Non Optimized Results.

* LAS=Left Motor Average Speed* RAS= Right Motor Average Speed* FE= Found Exit

We show in Table 2 the results of two experimentswith the evolutionary algorithm.

On the experiment #1 we can see that the top indivi-dual has a fitness value of 0.3568 and 40 active rules,comparing this with the experiment # 2 where the topindividual that has a fitness of 0.3566 and only 12 activerules, we can conclude that the solution of 12 rules ispreferred.


Experiment

91012

AverageStandard Deviation

123456789

AverageStandard Deviation

Fitness0.35680.35610.35610.35600.35600.35370.34940.34150.34150.33860.33860.33840.33840.33840.33840.33840.33840.33840.33790.3372

Generation179162257

19467120122148145849094961681686

129

Experiment # 1

Num_Rules4018124827348121269222121212121836

27 Rules FIS

10 Rules FIS

LAS

38.2640.4240.06

31.5135.5536.6636.6636.9135.4436.1433.4837.61

39.581.16

35.551.92

RAS

38.4640.6440.12

47.4354.3353.6853.6854.1852.5151.6649.5851.51

39.741.14

52.062.32

Time

60.3459.5060.70

55.7551.8055.4054.1049.9546.6549.8551.7655.15

60.180.62

52.273.10

LFE

YesYesYes

YesYesYesYesYesYesYesYesYes

Table 2. Reactive Control Optimized Results with the Evolutionary Algorithm.

Fitness0.35660.33400.33400.33400.33400.33400.33390.33390.33390.33390.33380.33380.33270.33020.33020.33020.33020.33020.33020.3302

Generation185069171011911942321321628145385140129159

Experiment # 2

Num_Rules12624818124181663218212816891624

Articles76

[4] Campion G., Bastin G. D'Andrea-Novel B., “StructuralProperties and Classification of Kinematic and DynamicModels of Wheeled Mobile Robots”,

, vol. 12, no. 1, February 1996.pp. 47-62.

[5] Cardenas S., Castillo O., Aguilar L. ,”Controlador deSeguimiento para un Robot Móvil empleando LógicaDifusa”, Tesis, División de Estudios y Posgrados e Inves-tigación, ITT, México, October of 2005. (in Spanish)

[6] Conde Bento L., Nunes U., Mendes A., Parent M. “Path-Tracking Controller of a bi-steerable Cybernetic Carusing Fuzzy Logic”.

, pp.1556-1561.

[7] Cupertino F., Giordano V., Naso D., Delfine L., ”Fuzzycontrol of a mobile robot”, Robotics & AutomationMagazine, IEEE, pp. 74-81.

[8] Erkkinen T., “Embedded Coder Robot NXT” http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=13399.

[9] Erkkinen T., “Embedded Coder Robot for LEGO® Mind-storms® NXT Rev. 3.03” http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=13399.

[10] Ishikawa S., “A Method of Indoor Mobile Robot Navi-gation by Fuzzy Control”,

, Osaka, Japan, 1991 pp. 1013-1018.[11] Thomson A., Baltes J., ”A path following system for

autonomous robots with minimal computing power”,University of Auckland, Private Bag 92019, Auckland,New Zealand, Technical Report, July 2001.

[12] Jang J.-S.R., Sun C.-T., Mizutani E., ”

”, Prentice Hall, 1997.[13] Kulkarni A., “Computer Vision and Fuzzy-Neural Sys-

tems”, Mayo, 2001 Prentice Hall PTR.[14] Leyden M., Toal D., Flanagan C., “A Fuzzy Logic Based

Navigation System for a Mobile Robot”, Proceedings ofAutomatisierungs Symposium, Wismar, Germany, 1999.

[15] Macek K., Petrovic I., Siegwart R., ”A control method forstable and smooth path following of mobile robots”,Proceedings of the 2nd European Conference on MobileRobots - ECMR 2005, Ancona, Italy, September 7-10,2005, pp. 128-133.

[16] Man K.F., “Genetic Algorithms: Concepts and Designs(Advanced Textbooks in Control and Signal Proces-sing)”, Springer, Corrected edition (March 30, 1999).

[17] Martínez R., Castillo O., Aguilar L., ”Control Inteligentede Robots Autónomos Móviles Bajo Pares PerturbadosUsando Lógica Difusa Tipo-2” Thesis, División de Estu-dios y Posgrados e Investigación, ITT, México, Febrerodel 2008.

[18] Meléndez A., Castillo O., Soria J., “Reactive Control ofa Mobile Robot in a Distributed Environment Using Fuz-zy Logic”, Fuzzy Information Processing Society, 2008.NAFIPS 2008. Annual Meeting of the North AmericanVolume, Issue, 19-22 May 2008, pp. 1-5.

[19] Payton D.W., Rosenblatt J.K., Keirsey D.M., ”Plan gui-ded reaction”, Systems, Man and Cybernetics, IEEETransactions on Volume 20, Issue 6, pp. 1370-1382.

[20] Peri V.M., Simon D. “Fuzzy logic control for an autono-mous robot” Fuzzy Information Processing Society,

IEEE Trans. on Robo-tics and Automation

Proceedings of ICAR 2003. The 11International Conference on Advanced Robotics

Proc. Int. Conf. Intell Robot.Syst.

Neuro-Fuzzy andSoft Computing a computacional approch to learning andmachine intelligence

th

2005. NAFIPS 2005. Annual Meeting of the NorthAmerican, pp. 337-342.

[21] Pishkenari H.N., Mahboobi S.H., Meghdari A., ”On theOptimum Design of Fuzzy Logic Controller for Tra-jectory Tracking Using Evolutionary Algorithms” Cyber-netics and Intelligent Systems, 2004 IEEE Conferenceon Publication Date: 1-3 Dec. 2004, vol.1, pp. 660-665.


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