StudyonAdaptiveCruiseControlStrategyforBattery ElectricVehicle

Research ArticleStudy on Adaptive Cruise Control Strategy for BatteryElectric Vehicle

Sheng Zhang 1 and Xiangtao Zhuan 12

1School of Electrical Engineering and Automation Wuhan University Wuhan 430072 China2Shenzhen Research Institute Wuhan University Shenzhen 518057 China

Correspondence should be addressed to Xiangtao Zhuan xtzhuanwhueducn

Received 2 September 2019 Revised 20 October 2019 Accepted 20 November 2019 Published 10 December 2019

Academic Editor Leonardo Acho

Copyright copy 2019 Sheng Zhang and Xiangtao Zhuan is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

is paper studies the control strategy for adaptive cruise control (ACC) system on a battery electric vehicle (BEV) in the car-following process and the highlight of this paper is that the regeneration braking of BEV is considered in the car-followingprocess e hierarchical control structure is adopted for the ACC system And the structure contains an upper controller and alower controller In the upper controller multiple objectives including the safety tracking comfort and energy consumption areoptimized by using the model predictive control (MPC) method In the lower controller the energy is recovered during brakingSo the energy economy is improved by reducing energy consumption and increasing energy recoverye proposed ACC strategyis evaluated in simulation experiment In the simulation experiment safe tracking for the front vehicle is guaranteed and thecomfort and the energy economy are improved greatly So the proposed adaptive cruise control strategy can make ACC morewidely used in BEVs

1 Introduction

With the increase in car ownership the traffic accidentsenvironmental pollution and oil shortage are getting worse[1] To solve these problems advanced driver-assistancesystems (ADAS) and battery electric vehicles (BEVs) are twoimportant vehicle technologies [2 3]

Among various ADAS technologies the adaptivecruise control (ACC) is an extension of traditional cruisecontrol which is used to improve the driving convenienceand reduce the driversrsquo mental burden [4] When there isno vehicle in front of a vehicle with ACC function (ownvehicle) the own vehicle is on the state of speed controlWhen a vehicle (front vehicle) occurs in front of the ownvehicle the own vehicle is on the state of distance controland the driving process of distance control is called thecar-following process in this paper During the car-fol-lowing process the own vehicle can ensure safety bytracking the velocity of front vehicle or keep an expectedspacing [5]

BEVs use battery as energy source and motor as drivingpower source so there are different dynamic characteristicsand energy limitations compared with fuel vehicles [6ndash8]e energy density of batteries for BEV is lower thanconventional diesel and gasoline which limits the distancetraveled by BEV from the full charge [8] And BEVs arecharged for a long time which puts higher demands for thedistance traveled by BEV on one charge erefore theimprovement of the energy economy for BEV is necessaryAnd BEV with ACC function is selected as the researchobject in the paper And the improvement of the energyeconomy for BEV is necessary And multiple objectives ofBEV during a car-following process including safetytracking comfort and energy economy are optimized

For the design of ACC controller various control al-gorithms that is the sliding mode control reinforcementlearning and fuzzy control algorithms have been applied[9ndash12] Among all kinds of control algorithms modelpredictive control (MPC) is an algorithm that is commonlyused for the study of ACC e advantages of the MPC

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 7971594 14 pageshttpsdoiorg10115520197971594

algorithm can be summarized as follows the optimizationfor control objectives is based on the model so the process ofmodeling is convenient various objectives can be integratedinto an MPC framework which can be easily handled by thedesigner the various objectives are optimized in a method ofonline receding horizon optimization which can compen-sate for errors due to inaccuracies in modeling [13ndash16]

Some studies related to the performance optimization ofthe ACC system for BEV have been done based on MPCMadhusudhanan [8] proposed an efficient cruise control toimprove driving range of the vehicle where the speed ref-erence for the own vehicle is obtained based on the up-coming traffic signal while safety is guaranteed bymaintaining a safe minimum spacing between two vehiclesZhang et al [17] proposed an energy efficiency control toincrease driving range And various traffic information wasfully considered in the process of optimization Schwickartet al [18] proposed an ecocruise controller to minimize theenergy consumption and a compromise between the energyconsumption and speed-reference tracking was achievedChen et al [19] proposed a cruise controller and energyconsumption was reduced with terrain information based onthe motor efficiency to increase the traveling distance Andthe velocity is selected as the optimized variable for reducingthe energy consumption

For the regenerative braking some researches have beenfinished A sliding mode controller was designed to co-ordinate the antilock braking force and regeneration brakingforce by Bera et al [20] Kim et al [21] applied the geneticalgorithm to increase the braking energy recovery based onensuring the vehicle stability and the expected road frictioncoefficient and yaw moment were considered Zhang et al[22] designed a fuzzy controller for the braking energyrecovery with the consideration of vehicle stability and thesimulation was performed in the ADVISOR platform Xuet al [23] designed the braking force distribution based onthe ideal distribution curve For increasing the brakingenergy recovery the battery states and vehicle states wereconsidered

However there are rare researches on combining ACCand braking energy recovery is paper focuses on it econtributions of this paper are that the braking energy re-covery is considered in the car-following process and theenergy economy during the car-following process is im-proved by reducing the energy consumption and improvingthe braking energy recovery

2 BEV Model with Braking Energy Recovery

e front-wheel drive BEV is chosen as the modeling objectand the structure of the front-wheel drive BEV is shown inFigure 1 In the braking process the motor drives the finaldrive to apply braking force to the front axle Since themotorbraking is affected by various factors it is needed to makecoordination for the hydraulic braking to complete thebraking process e hydraulic braking is implementedthrough controlling the hydraulic pressure adjustment unitof the electronic stability control (ESC) system e vehiclemodel is designed in Carsim software but the complete

powertrain model of BEV is not included in Carsim so theexternal models of motor and battery need to be added elithium battery and permanent magnet synchronous motorare selected for BEV in this paper

e internal resistance model is used to build the batterymodel [24] and the diagram for internal resistance model isshown in Figure 2 SOC is the state of charge of the batteryRint is the battery internal resistance Voc is the open circuitvoltage of battery Ic is the battery current and Uc is thebattery voltageRint is associated with SOC and Ice higherthe Rint the lower the battery efficiency for charging eregenerative braking of the motor is affected by the maxi-mum charging current of the battery When the SOC of thebattery is large the charging current allowed by the battery isvery small In order to limit the impact of excessive chargingcurrent on the battery life the regenerative braking of themotor cannot be performed when the SOC is large And thesimulations used in this paper do not involve long-termbraking process or cycle conditions erefore this paperdoes not set an additional model to estimate the SOC andtake the method to set the SOC to be the initial valueConsidering the influences of the battery on the own vehiclethe initial SOC is set to be 06

ere are many factors affecting the braking force of themotor is paper mainly considers the torque-speedcharacteristic [25] And the torque-speed characteristic isdefined in equation (1) where ωm is the angular velocity ofthe motor ω0 is the minimum velocity of the motor brakingtorque ωini is the minimum velocity of constant re-generation braking torque ωb is the base velocity of themotor ωend is the maximum speed of motor brakingtorque PB max is the maximum braking power of themotor and fm (ωm) is the correction for the regenerativebraking torque according to the motor efficiency And thediagram for the torque-speed characteristic is shown inFigure 3

TM max

0 ωm ltω0ωend leωm

9550PB max

ωb

ωini leωm leωb

9550PB max

ωm

fm ωm( 1113857 ω0 leωm leωini

9550PB max

ωm

ωb leωm leωend

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

During regenerative braking the motor can be used as agenerator to convert mechanical energy into electrical en-ergy And the battery pack is charged with the electric energyfrom the motor So the efficiency of energy recovery duringbraking process is related to the efficiencies of charging andmotor power generation

e power generation efficiency ηm of the motor is re-lated to torque Treb and the speed of the motor during theregenerative braking and it can be defined as

2 Mathematical Problems in Engineering

ηm UcIc

Trebωm

(2)

e power Pm generated by the motor can be defined as

Pm Trebωmηm Trebωm( 1113857 (3)

e charging efficiency of battery ηb is related to the SOCand Ic and the power for the charging Pb chg can be defined as

Pb chg IcUcηb Ic SOC( 1113857 (4)

Combining equations (2)ndash(4) the effective power ofenergy recovery for the battery pack during regenerativebraking process can be defined as

Pb chg Trebωmηm Trebωm( 1113857ηb Ic SOC( 1113857 (5)

e key parameters of the BEV model are presented inTable 1

3 Hierarchical Control Structure

eACC system in this paper adopts a hierarchical structurefor control and an upper controller and a lower controllerform the hierarchical structure [26] And the upper con-troller is used as a decision layer and a lower controller isused as a control layer e diagram of the hierarchicalcontrol structure is shown in Figure 4

When there is no vehicle in front of the own vehicle theown vehicle is in speed control mode and the own vehicledrives at the speed preset by the driver When there is avehicle in front of the own vehicle the own vehicle is in the

Drivingdirection

Hydraulicbraking

Finaldrive

Transmission

Regenerativebraking

Motor ESP

Batte

ry p

ack

MCU

VCU

BMS

ACCcontroller

Brakingcontroller

Power system

Hydraulic brake system

Pedal stroke simulatorRadar

Pressure sensorSpeed sensorPedal displacement sensor

Figure 1 e structural diagram of the BEV with regeneration braking

Mot

or re

gene

rativ

ebr

akin

g to

rque

TMmax

ω0 ωini ωb ωend

Motor speed

Figure 3 e diagram of the torque-speed characteristic

Rint

Voc

ExternalLoading

Uc Ic

Figure 2 e diagram of the internal resistance model

Mathematical Problems in Engineering 3

distance control mode and the upper controller for thedistance control mode contains a longitudinal car-followingmodel and an optimization algorithm for multiple objectivese upper controller calculates the optimized control com-mand for the acceleration to act on the lower controlleraccording to the motion state of the own vehicle and the frontvehicle e lower controller includes a switching logic and adistribution strategy for braking force e switching logiccontains a drive control strategy for motor an ESC-basedbrake control strategy and so on e distribution strategycontains distribution strategy of braking force for front axleand rear axle and distribution strategy of braking force formotor and hydraulic e lower controller tracks the controlcommand of acceleration based on the feedback signal of ownvehicle state and produces the signals of brake pressure andmotor torque and speed to act on the own vehicle

4 Lower Controller

In the hierarchical structure the upper controller is appliedto calculate the expected acceleration and the lower con-troller is used to determine that the own vehicle is in drivingmode or braking mode to track the control command edistribution strategy for braking force is an importantcomponent of the lower controller in this paper

e distribution strategy for braking force is the focus ofthe energy recovery system including the braking force

distribution for the front axle and rear axle which affects thestability of braking and the distribution for the motorbraking force and hydraulic braking force which affects theenergy recovery efficiency [23] Brake stability and energyrecovery efficiency need to be considered in coordination Tomaximize the recovery of braking energy the motor on frontaxle needs to provide more braking force as much as pos-sible However too much braking force on front axle willcause the vehicle to be unstable erefore the distributionstrategy for braking force is designed considering the re-strictions of the ECE regulations on the braking force of thefront axle and rear axle e distribution strategy of brakingforce in this paper is shown in Figure 5

Braking strength z is an important variable in the dis-tribution strategy for braking force it is the ratio of de-celeration adec to acceleration of gravity g and it is defined inequation (6) β is the distribution coefficient of braking forceand is defined in equation (7)

z adec

g (6)

β Fbf

Fb

Fbf

Fbf + Fbr

(7)

Considering the ECE regulations for braking stabilityrequirements some constraints should be put on β as follows

Table 1 Main parameters for the BEV model

Symbol Description ValuesMv Vehicle weight 1550 kgA Front area 228m2

Cw Drag coefficient 036fr Rolling resistance coefficient 0015ρair Air density 1206 kgm3

PM max Maximum power of the motor 87 KWSOCini Initial SOC 06Qbat Total battery capacity 93Ah

Adaptive cruise control

Upper controllerDriver input

Preset velocity

Accelerationcommand u(k)

Lower controllerSwitching logic

Distribution strategyFront axle and rear axleMotor and hydraulic

Dynamic controlcommands

Motor torque speedBraking pressure


Own vehile state

Own vehicle Front vehicle

Car-following plant

Motion stateOwn vehicle s v a jFront vehicle sf vf af

(i)(ii)

(i)(ii)

(i)(ii)

(a)(b)

(i)Motor controlBraking control

(a)(b)

(ii)

(i) Speed controlDistance control

Car-following modelMultiobjective optimization

(a)(b)

(i)(ii)

Figure 4 e diagram of the hierarchical control structure of the ACC system


βgeb + zhg1113872 1113873

L 015le zle 08

βle(z + 004) b + zhg1113872 1113873

07zL 01le zle 052

βge 1 minus(z + 004) a minus zhg1113872 1113873

07zL 01le zle 052

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)

e calculation of braking force for the front axle andrear axle is given below and the descriptions of the pa-rameters involved in the calculation process are shown inTable 2

When zlt z1 a lower limit of the braking force for thefront axle is not required in the regulation braking force isobtained only by motor braking on front axle and they aredefined as

Fbf Fb

Fbr 0(9)

When z1 lt zlt z2 braking forces on the front axle andrear axle are distributed along the lower limit for ECEregulations and they are defined as

Fbf Fb 1 minus(z + 004) l1 minus zhg1113872 1113873

07zL⎛⎝ ⎞⎠

Fbf Fb

(z + 004) l1 minus zhg1113872 1113873

07zL

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(10)

When z2 lt zlt z3 the braking strength is high the motorbraking achieves its maximum the braking force for frontaxle is constant and the hydraulic braking force for the rearaxle is increased and they are defined as

Fbf TB max middot ir

rw

Fbr Fb minus Fbf

(11)

When zgt z3 the motor brake is abandoned and thebraking forces on the front axle and rear axle are distributedalong the line of braking force distribution to ensure thesafety and take advantage of the ground attachment char-acteristics And they are defined in equation (12) In theprocess of braking force distribution if the motor brakingforce is insufficient it is compensated through the hydraulicbraking force

Fbf Fbβ

Fbr Fb(1 minus β)(12)

5 Upper Controller

51 Longitudinal Car-Following Model To design the uppercontroller the car-following model needs to be establishedfirstly In this paper the car-following model is based on thelongitudinal motion relationship of the front vehicle and theown vehicle

e spacing Δs and relative velocity vrel at moment k aredefined as follows

Δs(k) sf(k) minus s(k) (13)

vrel(k) vf(k) minus v(k) (14)

where sf and s are the distances of the front vehicle and theown vehicle respectively and vf and v are the speeds of thefront vehicle and the own vehicle respectively

Atmoment k+ 1 the distance of the front vehicle and theown vehicle is defined as follows

sf(k + 1) sf(k) + vf(k)Ts +12

af(k)T2s (15)

s(k + 1) s(k) + v(k)Ts +12

a(k)T2s (16)

where af and a are the acceleration of the front vehicle andthe own vehicle respectively and Ts is the sampling time

At moment k+ 1 the velocity of the front vehicle and theown vehicle is defined as follows

vf(k + 1) vf(k) + af(k)Ts (17)

v(k + 1) v(k) + a(k)Ts (18)

Table 2 Parameters in distribution strategy of braking force

Symbol DescriptionFb Total demand braking forceFbf Braking force of front axleFbr Braking force of rear axleL Wheelbasehg Centroid heightl1 Distance from centroid to front axleTB max Maximum braking torque of motorir Transmission ratio of main reducerrw Tire rolling radius2

1

3

4

Z1

Z2

Z3

0 2000 4000 6000 8000 10000 12000 14000Front axle braking force (N)

Rear

axle

bra

king

forc

e (N

)

8000

7000

6000

5000

4000

3000

2000

1000

0

Figure 5 e diagram of braking force distribution strategy


At moment k+ 1 the spacing and relative velocity aredefined as follows

Δs(k + 1) sf(k + 1) minus s(k + 1) (19)

vrel(k + 1) vf(k + 1) minus s(k + 1) (20)

Combining equations (13)ndash(16) and (19) the followingequation can be obtained

Δs(k + 1) Δs(k) + vrel(k)Ts +12

af(k)T2s minus

12

a(k)T2s

(21)

Combining equations (14) (17) (18) and (20) thefollowing equation can be obtained

vrel(k + 1) vrel(k) + af(k)Ts minus a(k)Ts (22)

When the upper controller for the ACC system isdesigned due to the foundation of the lower controller itcan be considered that the actual acceleration of the ownvehicle a and control command for acceleration (also calledexpected acceleration) u satisfy the following relationship[13 26]

a(k + 1) 1 minusTs

τ1113874 1113875a(k) +

Ts

τu(k) (23)

where u is the control command for acceleration and τ is thetime constant of the lower controller

e rate of change of acceleration is also called jerk andthe jerk at moment k can be defined as follows

j(k) a(k) minus a(k minus 1)

Ts

(24)

At moment k+ 1 the jerk can be defined as follows

j(k + 1) a(k + 1) minus a(k)

Ts

(25)

Combining equations (23) and (25) the followingequation can be obtained

j(k + 1) minus1τ

a(k) +1τ

u(k) (26)

e spacing speed of the own vehicle relative velocityacceleration of the own vehicle and jerk for the own vehicleare selected as the state vector and they are defined as

x(k) Δs(k) v(k) vrel(k) a(k) j(k)1113858 1113859T (27)

e acceleration for the front vehicle is selected as thedisturbance and it is defined as

w(k) af(k) (28)

Combining equations (18) (21)ndash(23) and (26) the car-following model in the longitudinal direction is defined

x(k + 1) Ax(k) + Bu(k) + Gw(k) (29)

where

A

1 0 Ts minus12T2s 0

0 1 0 Ts 0

0 0 1 minus Ts 0

0 0 0 1 minusTs

τ0

0 0 0 minus1τ

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B

0

0

0

Ts

τ

1τ

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

G

12T2s

0

Ts

0

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(30)

52 Model Predictive Control (MPC) for Multiple ObjectivesIn the multiobjective-optimized upper controller thecontrol objectives enable the own vehicle to guaranteesafety tracking comfort and energy economy in thedriving process To achieve these control objectives themultiple objectives are analyzed based on the car-followingmodel e multiple objectives are transformed into thecorresponding system constraints and performance in-dicators And the optimization for multiple objectives inthe driving process is finally transformed into a constrainedoptimization propositionΔsdes is the expected spacing obtained from the constant

time headway (CTH) spacing policy δ is the differencebetween the real spacing and the expected spacing and Δsdesand δ at moment k can be defined


Δsdes(k) d0 + th middot v(k) (31)

δ(k) Δs(k) minus Δsdes(k) (32)

where d0 is the fixed distance between the two vehicles whenthe vehicle speed is low and zero and th is the time headway

To ensure the tracking in the car-following process theactual spacing between the two vehicles approaches the ex-pected spacing calculated by the spacing strategy and thevelocity of the own vehicle should be close to the velocity ofthe front vehicle that is the two vehicles are in a relativelystatic state [26]

objectives δ(k)⟶ 0 as k⟶infin

vrel(k)⟶ 0 as k⟶infin1113896 (33)

To improve the comfort during the car-following pro-cess the range of fluctuation for acceleration and jerk shouldbe minimized

objectives min |a(k)|

min |j(k)|1113896 (34)

From above analysis the spacing error relative velocityacceleration of the own vehicle and jerk of the own vehicleare chosen as the performance vector and the performancevector is defined

y(k) δ(k) vrel(k) a(k) j(k)1113858 1113859T (35)

e following relationship can be established betweenthe performance vector and the state variable

y(k) Cx(k) minus Z (36)

where

C

1 minus th 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

d0000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)

During the car-following process a smooth system re-sponse is preferred To smooth the response the exponentialdecay function is introduced to be reference trajectory ofperformance vector

e coefficient of the error of spacing in reference tra-jectory is defined in the following equation and other co-efficients can be defined in a similar way

δr(k + i) δ(k) + δdes(k) minus δ(k)1113858 1113859 1 minus eminus iTsαδ( )1113876 1113877

δ(k) +[0 minus δ(k)] 1 minus eminus iTsαδ( )1113876 1113877

ρiδδ(k)

ρδ eminus Tsαδ( ) 0lt ρδ lt 1

(38)

where δr is the reference trajectory for the error of spacingand α is the time constant of the reference trajectory for theerror of spacing

e system response is smoothed as follows

yr(k + i)

ρiδρi

vrel

ρia

ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦y(k) (39)

where ρδ ρvrel ρa and ρj are the coefficients in reference

trajectory ρδ is the coefficient of the spacing error ρvrelis the

coefficient of relative velocity ρa is the coefficient of theacceleration of the own vehicle and ρj is the coefficient ofthe jerk of the own vehicle

e values of these coefficients are between 0 and 1Along the reference trajectory the performance vector ap-proaches zero smoothly rather than approaching zerodirectly

As for the energy economy it is related to the acceler-ation And the acceleration is determined by the controlcommand of acceleration erefore the control commandof acceleration is selected as the performance index of theenergy economy [27] To improve the energy economy theabsolute value of control command should be minimized

objective min |u(k)| (40)

No matter what control algorithm is used the safety isthe primary objective of an ACC system Although we canguarantee a safe expected spacing through the spacingstrategy the collision is likely to happen before reaching theexpected spacing erefore for the purpose of ensuring thesafety of two vehicles throughout the driving process theactual vehicle spacing must be constrained as follows

Δs(k) sp(k) minus s(k)gedc (41)

where dc is the minimum safe spacing between two vehiclesTaking into account the limitations of the vehicles own

capacity it needs to constrain the velocity acceleration jerkand acceleration command for the own vehicle e con-straints can be defined

vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(42)

Because of the advantages of MPC in achieving multi-objective optimization [27ndash29] the MPC is applied into themultiobjective optimization of the ACC system

Predictive form for the state vector and performancevector are defined as follows

1113954Xp(k + p | k) Ax(k) + BU(k + m) + GW(k + p) (43)

1113954Yp(k + p | k) Cx(k) + DU(k + m) + EW(k + p) minus Z

(44)


where

1113954Xp(k + p | k)

1113954xp(k + 1 | k)

1113954xp(k + 2 | k)

⋮

1113954xp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1113954Yp(k + p | k)

1113954yp(k + 1 | k)

1113954yp(k + 2 | k)

⋮

1113954yp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

U(k + m)

u(k)

u(k + 1)

⋮

u(k + m minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

W(k + p)

w(k)

w(k + 1)

⋮

w(k + p minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

A

A

A2

⋮

Ap

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B

B 0 middot middot middot 0

AB B ⋱ 0

⋮ ⋮ ⋱ ⋮

Apminus 1B Apminus 2B middot middot middot Apminus mB

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

G

G 0 middot middot middot 0

AG G ⋱ ⋮

⋮ ⋮ ⋱ 0

Apminus 1G Apminus 2G middot middot middot G

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

C

CA

CA2

⋮

CAp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

D

CB 0 middot middot middot 0

CAB CB ⋱ 0

⋮ ⋮ ⋱ ⋮

CApminus 1B CApminus 2B middot middot middot CApminus mB

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

E

CG 0 middot middot middot 0

CAG CG ⋱ ⋮

⋮ ⋮ ⋱ 0

CApminus 1G CApminus 2G middot middot middot CG

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

Z

Z

⋮

Z

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)

where xp(k+ i | k) is the predictive value of the state vectorfor k+ i moment at the moment k yp(k+ i | k) is the pre-dictive value of the performance vector for k+ i moment atthe moment k U(k+m) is the matrix for the sequence of thecontrol command p is the predictive horizon and m is thecontrol horizon

And considering the different objectives in equations(33) (34) and (40) and the reference trajectory in equation(39) the discretized objective function based onMPC can beobtained

J 1113944

p

i1yp(k + i | k) minus yr(k + i)1113960 1113961

TQ yp(k + i | k) minus yr(k + i)1113960 1113961

+ 1113944mminus 1

j0u(k + j)

TRu(k + j)

(46)where Q and R are the weight matrices and u(k+ i) is thecontrol command at moment k+ i

Combining the equations (44) and (46) the followingequation can be obtained

J VTQV + U(k + m)

TRU(k + m) (47)

whereV Cx(k) + DU(k + m) + EW(k + p) minus Z minus ΦCx(k) +ΦZ

Q

Q middot middot middot 0⋮ ⋱ ⋮0 middot middot middot Q

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

R

R middot middot middot 0⋮ ⋱ ⋮0 middot middot middot R

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Φ

Ψ1Ψ2⋮Ψp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ψi

ρiδ 0 0 00 ρi

vrel0 0

0 0 ρia 0

0 0 0 ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(48)

Expand equation (47) to retain the items related toU(k+m) the following equation can be obtained

J U(k + m)T

R + DTQD1113874 1113875U(k + m)

+ 21113882x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD1113883U(k + m)

(49)All the constraints in this paper can be summarized in

the following form


Δx(k)gedc

vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(50)

Convert equation (50) into the form of matrix inequalitythe following equation can be obtained

Mle L 1113954Xp(k + p)leN

U(k + m)leUmax

minus U(k + m)le minus Umin

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(51)

where

M

dc

vmin

amin

jmin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

Inf

vmax

amax

jmax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L

1 0 0 0 00 1 0 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L

L 0 0 middot middot middot 0 00 L 0 0 middot middot middot 00 0 ⋱ 0 middot middot middot 00 middot middot middot 0 ⋱ 0 00 0 middot middot middot 0 L 00 0 middot middot middot 0 0 L

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ptimesp

M

M

M

⋮M

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

N

N

⋮N

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umax

umax

⋮umax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umin

umin

⋮umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(52)

Combining equations (43) and (51) the followingequation for constraints can be obtained

ΩU(k + m)leT (53)

where

Ω LB minus LB I minus I1113858 1113859T

T

N minus LGW(k + p) minus LAx(k)

minus M + LGW(k + p) + LAx(k)

Umax

minus Umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(54)

e objective function in equation (49) combined withthe constraints in equations (53) can be converted to anoptimization problem in the following equation that can besolved by quadratic programming [30 31]

min U(k + m)TKU(k + m) + 2SU(k + m)1113966 1113967

st ΩU(k + m)leT(55)

where

K R + DTQD

S x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD

(56)

Optimal control variable Ulowast(k + m) can be solved fromthe quadratic programming problem in equation (55) Andonly the first component of Ulowast(k + m) can be applied to theACC system as the optimal acceleration command And atthe next moment the above process is repeated is reflectsthe receding horizon optimization in MPC

6 Methods

To evaluate the performances of the proposed ACC strategytwo different strategies are compared e control strategystudied in this paper contains comfort energy economysafety and tracking And the strategy that contains safetyand tracking is the contrast strategy In the contrast controlstrategy the braking energy recovery is not considered in thelower controller or the BEV model the coefficients for R iszero the optimized reference trajectories are not applied tothe objective function and there are no strict constraints onjerke abbreviations for the proposed control strategy andcontrast control strategy are BER_CEST and NO_STrespectively

e minimum safe spacing is an important indicator forthe safety and when the spacing is bigger than it the drivingprocess is considered safe e capability of adjusting thedifference of spacing to zero and the capability of regulatingthe relative velocity to zero are regarded as the measurementof the tracking e maximum value of jerkrsquos absolute valueis an important indicator for the comfort during the drivingprocess and the limit of the indicator for comfort is 3ms3Energy economy is estimated by the change of SOC e


strategies are designed with the MatlabSimulink and thesimulation experiment is performed combined with theCarsim platform

Scenario in simulation is set as follows (1) e speed ofthe front vehicle is changing and (2) cut in ese twoscenarios are representative scenarios Wherein conven-tional driving process for the two vehicles is shown inscenario 1 and the urgent driving process for the two ve-hicles is shown in scenario 2 Settings for two simulationscenarios are shown in Table 3 where Δs ini is the initialvehicle spacing v_ini and vf_ini are the initial speed for theown vehicle and the front vehicle respectively and a_amp isthe amplitude of acceleration for the front vehicle e mainparameters for the multiobjective optimization algorithmare listed in Table 4

7 Simulation Experiment and Discussion

71 Scenario 1 In real life following a front vehicle with avariable speed is a familiar traffic scenario is scenariomainly examines the capability of speed adjustment andtracking for the own vehicle when the speed of the frontvehicle changes on a single lane e simulation results inscenario 1 are shown in Figure 6 From Figure 6(a) it can beseen that the vehicle spacing is greater than minimum safespacing in two control strategies so the safety is ensured inboth control strategies From Figures 6(a) and 6(b) thetracking can be ensured in both control strategies For thedesired spacing the tracking ability is better in NO_ST andfor the speed of the front vehicle the tracking ability is betterin BER_CEST is is a compromise among various controlobjectives in BER_CEST

From Figure 6(c) the fluctuation range for acceleration isbigger in NO_ST than BER_CEST while the curve of theacceleration in BER_CEST is relatively smooth FromFigure 6(d) the maximum value of the jerkrsquos absolute value inNO_ST is 1866ms3 which exceeds 3ms3 However themaximum value of the jerkrsquos absolute value in BER_CEST isalways within the 3ms3 erefore the comfort in BER_C-EST is improved compared with the NO_ST e reasons forthis are that the jerk is strictly constrained and the optimizedreference trajectory are applied to improve the comfort inBER_CEST Driving is more stable while comfort is improvederefore the driving stability is also improved because of theintroduction of the optimized reference trajectory and theapplication of the strict constraints on jerk From Figure 6(e)it is shown that the battery power in BER_CEST changesbetween positive and negative However the battery power inNO_ST changes between zero and positive is is becausethe energy is recovered during braking process in BER_CESTFrom Figure 6(f) the change of SOC for two strategies is00020 and 00042 respectively e improvement of theenergy economy for BER_CEST is 5203 compared withNO_STe reasons for this are that the energy consumptionis optimized in the upper controller and the braking energyrecovery is considered in the lower controller in BER_CESTerefore the energy economy is improved in BER_CEST

From the above analysis BER_CEST adopts the opti-mized reference trajectory and strict constraints on jerk to

improve the comfort and the energy economy is consideredboth in the upper controller and the lower controller SoBER_CEST can obtain better comfort and energy economycompared with NO_ST based on ensuring the safety andtracking

72 Scenario 2 In the cut in scenario in the driving processof the own vehicle the front vehicle of the adjacent lanesuddenly changes lane and the front vehicle is inserted infront of the own vehicle e simulation results of scenario 2are shown in Figure 7 From Figure 7(a) because the spacingbetween two vehicles is bigger than 5m the driving pro-cesses both are safe in two control strategies FromFigures 7(a) and 7(b) the own vehicle can track the desiredvehicle spacing and the velocity of front vehicle in twostrategies For the desired spacing the tracking ability isbetter in NO_ST and for the speed of the front vehicle thetracking abilities are closer in both strategies is is acompromise among various control objectives inBER_CEST

From Figure 7(c) the fluctuation range for the accel-eration is bigger in NO_ST while the curve of acceleration isrelatively smooth in BER_CEST From Figure 7(d) themaximum value of the jerkrsquos absolute value in NO_ST is1649ms3 which exceeds 3ms3 But the maximum valueof the jerkrsquos absolute value in BER_CEST is always within3ms3 e comfort in BER_CEST is improved comparedwith NO_ST e reasons for this are that the jerk is strictlyconstrained and the optimized reference trajectory is ap-plied to improve the comfort Driving is more stable whilecomfort is improved erefore the driving stability is alsoimproved because of the introduction of the optimized

Table 3 Settings for two simulation scenarios

Scenario Δs ini (m) v_ini (ms) vf_ini (ms) a_amp (ms2)

1 50 10 15 22 30 15 10 2

Table 4 Parameters in the simulation process

Symbol ValuesTs 02 sτ 015 sd0 7mdc 5mvmin 0msvmax 36msamin minus 55ms2

amax 25ms2

umin minus 55ms2

umax 25ms2

jmin minus 3ms3

jmax 3ms3

ρδ ρvrel ρa ρj 094

Q diag 1 10 1 1

R 1p 10m 5


0

10

20

30

40

50

60

70

80Sp

acin

g (m

)

Time (s)

BER_CEST_ΔsBER_CEST_Δsdes

NO_ST_ΔsNO_ST_Δsdes

0 10 20 30 40 50

(a)

8

10

12

14

16

18

20

22

Spee

d (m

s)

Front vehicleBER_CESTNO_ST

Time (s)0 10 20 30 40 50

(b)

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash40

ndash20

0

20

40

60

80

100

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

0596

05965

0597

05975

0598

05985

0599

05995

06

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f)

Figure 6 Simulation results of scenario 1 (a) Spacing response (b) Speed response (c) Acceleration response (d) Jerk response (e) Batterypower (f ) SOC


Time (s)

0

10

20

30

40

50Sp

acin

g (m

)



0 10 20 30 40 50

(a)

8

9

10

11

12

13

14

15

16

17

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash30

ndash10

10

30

50

70

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

05975

05995

06015

06035

06055

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f )



reference trajectory and the application of the strict con-straints on jerk From Figure 7(e) it is shown that thebattery power in BER_CEST changes between positiveand negative However the battery power in NO_STchanges between zero and positive is is because thebraking energy recovery is considered in the lower con-troller From Figure 7(f ) the change of SOC for twostrategies is 000096 and 00022 respectively e im-provement of the energy economy for BER_CEST is5573 compared with NO_ST After the front vehicleperforms the cut in the braking energy is recoveredduring braking process and the SOC is bigger than theinitial SOC is is because the kinetic energy of BEV isrecovered through the regenerative braking during thebraking process in BER_CEST

In summary BER_CEST adopts the optimized refer-ence trajectories and strict constraints on jerk to improvethe comfort and the energy economy is considered both inthe upper controller and the lower controller SoBER_CEST can obtain better comfort and energy economycompared with NO_ST based on ensuring the safety andtracking

8 Conclusion

In this paper a hierarchical control architecture is adopted forthe proposed ACC strategy on BEV and the highlight of thispaper is that the braking energy recovery is considered in thecar-following process In the proposed control strategy thesafety tracking and comfort are considered in the uppercontroller and the energy economy is considered both in theupper controller and lower controller Some conclusions canbe obtained as follows in the upper controller the acceler-ation command is optimized in the objective function ofMPCto reduce the energy consumption In the lower controller thebraking energy is recovered during the braking process So theenergy economy is improvede proposed ACC strategy canimprove the comfort for passengers and improve the energyeconomy for the car owner so it can promote the wideapplication of ACC in BEV

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the Basic Research Project of theKnowledge Innovation Program in Shenzhen City (Grantno JCYJ20170818144449801)

References

[1] Q P Liu and C P Tang ldquoEnvironmental impact assessmentof magnesium alloy automobile hub based on life cycle

assessmentrdquo Journal of Central South University vol 25 no 8pp 1870ndash1878 2018

[2] Y Luo T Chen and K Li ldquoMulti-objective decoupling al-gorithm for active distance control of intelligent hybridelectric vehiclerdquo Mechanical Systems and Signal Processingvol 64-65 pp 29ndash45 2015

[3] Y Chen and J Wang ldquoDesign and evaluation on electricdifferentials for over-actuated electric ground vehicleswith four independent in-wheel motorsrdquo IEEE Trans-actions on Vehicular Technology vol 61 no 4 pp 1534ndash1542 2012

[4] Y Luo T Chen S Zhang and K Li ldquoIntelligent hybridelectric vehicle ACC with coordinated control of trackingability fuel Economy and ride comfortrdquo IEEE Transactionson Intelligent Transportation Systems vol 16 no 4pp 2303ndash2308 2015

[5] L H Yang X Q Zhang J K Zhang and J T Liu ldquoeresearch of car-following model based on real-time maximumdecelerationrdquo Mathematical Problems in Engineeringvol 2015 Article ID 642021 9 pages 2015

[6] X Ding H Guo R Xiong F Chen D Zhang and C GeradaldquoA new strategy of efficiency enhancement for traction sys-tems in electric vehiclesrdquo Applied Energy vol 205 pp 880ndash891 2017

[7] R Xiong Q Yu L Y Wang and C Lin ldquoA novel method toobtain the open circuit voltage for the state of charge oflithium ion batteries in electric vehicles by using H infinityfilterrdquo Applied Energy vol 207 pp 346ndash353 2017

[8] A K Madhusudhanan ldquoA method to improve an electricvehicles range efficient Cruise Controlrdquo European Journal ofControl vol 48 pp 83ndash96 2019

[9] B Ganji A Z Kouzani S Y Khoo and M Shans-ZahraeildquoAdaptive cruise control of a HEV using sliding mode con-trolrdquo Expert Systems with Applications vol 41 no 2pp 607ndash615 2014

[10] R Abdullah A Hussain K Warwick and A Zayed ldquoAu-tonomous intelligent cruise control using a novel multiple-controller framework incorporating fuzzy-logic-basedswitching and tuningrdquo Neurocomputing vol 71 no 13ndash15pp 2727ndash2741 2008

[11] C Desjardins and B Chaib-draa ldquoCooperative adaptive cruisecontrol a reinforcement learning approachrdquo IEEE Trans-actions on Intelligent Transportation Systems vol 12 no 4pp 1248ndash1260 2011

[12] A Weibmann D Gorges and X H Lin ldquoEnergy-optimaladaptive cruise control combining model predictive controland dynamic programmingrdquo Control Engineering Practicevol 72 pp 125ndash137 2018

[13] V L Bageshwar W L Garrard and R Rajamani ldquoModelpredictive control of transitional maneuvers for adaptivecruise control vehiclesrdquo IEEE Transactions on VehicularTechnology vol 53 no 5 pp 1573ndash1585 2004

[14] C M Filho M H Terra and D FWolf ldquoSafe optimization ofhighway traffic with robust model predictive control-basedcooperative adaptive cruise controlrdquo IEEE Transactions onIntelligent Transportation Systems vol 18 no 11 pp 3193ndash3203 2017

[15] M M Brugnolli B A Angelico and A A M LaganaldquoPredictive adaptive cruise control using a customized ECUrdquoIEEE Access vol 7 pp 55305ndash55317 2019

[16] B Sakhdari and N L Azad ldquoAdaptive tube-based nonlinearMPC for economic autonomous cruise control of plug-inhybrid electric vehiclesrdquo IEEE Transactions on VehicularTechnology vol 67 no 12 pp 11390ndash11401 2018


[17] S Zhang Y Luo K Li and V Li ldquoReal-time energy-efficientcontrol for fully electric vehicles based on an explicit modelpredictive control methodrdquo IEEE Transactions on VehicularTechnology vol 67 no 6 pp 4693ndash4701 2018

[18] T Schwickart H Voos J-R Hadji-Minaglou andM Darouach ldquoA fast model-predictive speed controller forminimised charge consumption of electric vehiclesrdquo AsianJournal of Control vol 18 no 1 pp 133ndash149 2016

[19] Y Chen X D Li C Wiet and J M Wang ldquoEnergy man-agement and driving strategy for in-wheel motor electricground vehicles with terrain profile previewrdquo IEEE Trans-actions on Industrial Informatics vol 10 no 3 pp 1938ndash19472014

[20] T K Bera K Bhattacharya and A K Samantarary ldquoBondgraph model-based evaluation of a sliding mode controller fora combined regenerative and antilock braking systemrdquoProceedings of the Institution of Mechanical Engineers Part IJournal of Systems and Control Engineering vol 225 no 17pp 918ndash934 2011

[21] D H Kim J M Kim and S H Hwang ldquoOptimal braketorque distribution for a four-wheeldrive hybrid electric ve-hicle stability enhancementrdquo Proceedings of the Institution ofMechanical Engineers Part I Journal of Systems and ControlEngineering vol 221 no 11 pp 1357ndash1366 2007

[22] J M Zhang B Y Song and S M Cui ldquoFuzzy logic approachto regenerative braking systemrdquo in Proceedings of the In-ternational Conference on Intelligent Human-Machine Sys-tems and Cybernetics pp 451ndash454 Hangzhou China 2009

[23] G Xu W Li K Xu and Z Song ldquoAn intelligent regenerativebraking strategy for electric vehiclesrdquo Energies vol 4 no 9pp 1461ndash1477 2011

[24] A Abdollahi X Han G V Avvari et al ldquoOptimal batterycharging part I minimizing time-to-charge energy loss andtemperature rise for OCV-resistance battery modelrdquo Journalof Power Sources vol 303 pp 388ndash398 2016

[25] L Li Y Zhang C Yang B Yan and C Marina MartinezldquoModel predictive control-based efficient energy recoverycontrol strategy for regenerative braking system of hybridelectric busrdquo Energy Conversion and Management vol 111pp 299ndash314 2016

[26] S Li K Li R Rajamani and J Wang ldquoModel predictivemulti-objective vehicular adaptive cruise controlrdquo IEEETransactions on Control Systems Technology vol 19 no 3pp 556ndash566 2011

[27] R N Dang H Chaoche Q Zhang K Q Li and Y S LildquoACC of electric vehicles with coordination control of fueleconomy and tracking safetyrdquo in Proceedings of the 2012 IEEEIntelligent Vehicles Symposium pp 240ndash245 Alcala deHenares Spain June 2012

[28] C Zhai Y Liu and F Luo ldquoA switched control strategy ofheterogeneous vehicle platoon for multiple objectives withstate constraintsrdquo IEEE Transactions on Intelligent Trans-portation Systems vol 20 no 5 pp 1883ndash1896 2019

[29] X K Xu J Peng R Zhang et al ldquoAdaptive model predictivecontrol for cruise control of high-speed trains with time-varying parametersrdquo Journal of Advanced Transportationvol 2019 Article ID 7261726 11 pages 2019

[30] Z Wu X H Xia and B Zhu ldquoModel predictive control forimproving operational efficiency of overhead cranesrdquo Non-linear Dynamics vol 79 no 4 pp 2639ndash2657 2015

[31] Q Wang B Ayalew and T Weiskircher ldquoPredictive ma-neuver planning for an autonomous vehicle in public highwaytrafficrdquo IEEE Transactions on Intelligent Transportation Sys-tems vol 20 no 4 pp 1303ndash1315 2019


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Submit your manuscripts atwwwhindawicom

algorithm can be summarized as follows the optimizationfor control objectives is based on the model so the process ofmodeling is convenient various objectives can be integratedinto an MPC framework which can be easily handled by thedesigner the various objectives are optimized in a method ofonline receding horizon optimization which can compen-sate for errors due to inaccuracies in modeling [13ndash16]

Some studies related to the performance optimization ofthe ACC system for BEV have been done based on MPCMadhusudhanan [8] proposed an efficient cruise control toimprove driving range of the vehicle where the speed ref-erence for the own vehicle is obtained based on the up-coming traffic signal while safety is guaranteed bymaintaining a safe minimum spacing between two vehiclesZhang et al [17] proposed an energy efficiency control toincrease driving range And various traffic information wasfully considered in the process of optimization Schwickartet al [18] proposed an ecocruise controller to minimize theenergy consumption and a compromise between the energyconsumption and speed-reference tracking was achievedChen et al [19] proposed a cruise controller and energyconsumption was reduced with terrain information based onthe motor efficiency to increase the traveling distance Andthe velocity is selected as the optimized variable for reducingthe energy consumption

For the regenerative braking some researches have beenfinished A sliding mode controller was designed to co-ordinate the antilock braking force and regeneration brakingforce by Bera et al [20] Kim et al [21] applied the geneticalgorithm to increase the braking energy recovery based onensuring the vehicle stability and the expected road frictioncoefficient and yaw moment were considered Zhang et al[22] designed a fuzzy controller for the braking energyrecovery with the consideration of vehicle stability and thesimulation was performed in the ADVISOR platform Xuet al [23] designed the braking force distribution based onthe ideal distribution curve For increasing the brakingenergy recovery the battery states and vehicle states wereconsidered

However there are rare researches on combining ACCand braking energy recovery is paper focuses on it econtributions of this paper are that the braking energy re-covery is considered in the car-following process and theenergy economy during the car-following process is im-proved by reducing the energy consumption and improvingthe braking energy recovery

2 BEV Model with Braking Energy Recovery

e front-wheel drive BEV is chosen as the modeling objectand the structure of the front-wheel drive BEV is shown inFigure 1 In the braking process the motor drives the finaldrive to apply braking force to the front axle Since themotorbraking is affected by various factors it is needed to makecoordination for the hydraulic braking to complete thebraking process e hydraulic braking is implementedthrough controlling the hydraulic pressure adjustment unitof the electronic stability control (ESC) system e vehiclemodel is designed in Carsim software but the complete

powertrain model of BEV is not included in Carsim so theexternal models of motor and battery need to be added elithium battery and permanent magnet synchronous motorare selected for BEV in this paper

e internal resistance model is used to build the batterymodel [24] and the diagram for internal resistance model isshown in Figure 2 SOC is the state of charge of the batteryRint is the battery internal resistance Voc is the open circuitvoltage of battery Ic is the battery current and Uc is thebattery voltageRint is associated with SOC and Ice higherthe Rint the lower the battery efficiency for charging eregenerative braking of the motor is affected by the maxi-mum charging current of the battery When the SOC of thebattery is large the charging current allowed by the battery isvery small In order to limit the impact of excessive chargingcurrent on the battery life the regenerative braking of themotor cannot be performed when the SOC is large And thesimulations used in this paper do not involve long-termbraking process or cycle conditions erefore this paperdoes not set an additional model to estimate the SOC andtake the method to set the SOC to be the initial valueConsidering the influences of the battery on the own vehiclethe initial SOC is set to be 06

ere are many factors affecting the braking force of themotor is paper mainly considers the torque-speedcharacteristic [25] And the torque-speed characteristic isdefined in equation (1) where ωm is the angular velocity ofthe motor ω0 is the minimum velocity of the motor brakingtorque ωini is the minimum velocity of constant re-generation braking torque ωb is the base velocity of themotor ωend is the maximum speed of motor brakingtorque PB max is the maximum braking power of themotor and fm (ωm) is the correction for the regenerativebraking torque according to the motor efficiency And thediagram for the torque-speed characteristic is shown inFigure 3

TM max

0 ωm ltω0ωend leωm

9550PB max

ωb

ωini leωm leωb

9550PB max

ωm

fm ωm( 1113857 ω0 leωm leωini

9550PB max

ωm

ωb leωm leωend

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

During regenerative braking the motor can be used as agenerator to convert mechanical energy into electrical en-ergy And the battery pack is charged with the electric energyfrom the motor So the efficiency of energy recovery duringbraking process is related to the efficiencies of charging andmotor power generation

e power generation efficiency ηm of the motor is re-lated to torque Treb and the speed of the motor during theregenerative braking and it can be defined as


ηm UcIc

Trebωm

(2)











Drivingdirection

Hydraulicbraking

Finaldrive

Transmission

Regenerativebraking

Motor ESP

Batte

ry p

ack

MCU

VCU

BMS

ACCcontroller

Brakingcontroller

Power system





Mot

or re

gene

rativ

ebr

akin

g to

rque

TMmax

ω0 ωini ωb ωend

Motor speed


Rint

Voc

ExternalLoading

Uc Ic




4 Lower Controller





z adec

g (6)

β Fbf

Fb

Fbf

Fbf + Fbr

(7)








Preset velocity







Own vehile state


Car-following plant


(i)(ii)

(i)(ii)

(i)(ii)

(a)(b)


(a)(b)

(ii)



(a)(b)

(i)(ii)



βgeb + zhg1113872 1113873

L 015le zle 08

βle(z + 004) b + zhg1113872 1113873

07zL 01le zle 052


07zL 01le zle 052

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)



Fbf Fb

Fbr 0(9)



07zL⎛⎝ ⎞⎠

Fbf Fb

(z + 004) l1 minus zhg1113872 1113873

07zL

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(10)



rw

Fbr Fb minus Fbf

(11)


Fbf Fbβ


5 Upper Controller







sf(k + 1) sf(k) + vf(k)Ts +12

af(k)T2s (15)

s(k + 1) s(k) + v(k)Ts +12

a(k)T2s (16)



vf(k + 1) vf(k) + af(k)Ts (17)

v(k + 1) v(k) + a(k)Ts (18)



1

3

4

Z1

Z2

Z3


Rear

axle

bra

king

forc

e (N

)

8000

7000

6000

5000

4000

3000

2000

1000

0




Δs(k + 1) sf(k + 1) minus s(k + 1) (19)




af(k)T2s minus

12

a(k)T2s

(21)




a(k + 1) 1 minusTs

τ1113874 1113875a(k) +

Ts

τu(k) (23)




Ts

(24)


j(k + 1) a(k + 1) minus a(k)

Ts

(25)


j(k + 1) minus1τ

a(k) +1τ

u(k) (26)




w(k) af(k) (28)


x(k + 1) Ax(k) + Bu(k) + Gw(k) (29)

where

A

1 0 Ts minus12T2s 0

0 1 0 Ts 0

0 0 1 minus Ts 0

0 0 0 1 minusTs

τ0

0 0 0 minus1τ

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B

0

0

0

Ts

τ

1τ

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

G

12T2s

0

Ts

0

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(30)









vrel(k)⟶ 0 as k⟶infin1113896 (33)



min |j(k)|1113896 (34)


y(k) δ(k) vrel(k) a(k) j(k)1113858 1113859T (35)



where

C

1 minus th 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

d0000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)





ρiδδ(k)


(38)



yr(k + i)

ρiδρi

vrel

ρia

ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦y(k) (39)











vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(42)





(44)


where

1113954Xp(k + p | k)

1113954xp(k + 1 | k)

1113954xp(k + 2 | k)

⋮

1113954xp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1113954Yp(k + p | k)

1113954yp(k + 1 | k)

1113954yp(k + 2 | k)

⋮

1113954yp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

U(k + m)

u(k)

u(k + 1)

⋮

u(k + m minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

W(k + p)

w(k)

w(k + 1)

⋮

w(k + p minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

A

A

A2

⋮

Ap

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B


AB B ⋱ 0

⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

G


AG G ⋱ ⋮

⋮ ⋮ ⋱ 0


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

C

CA

CA2

⋮

CAp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

D


CAB CB ⋱ 0

⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

E


CAG CG ⋱ ⋮

⋮ ⋮ ⋱ 0


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

Z

Z

⋮

Z

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)



J 1113944

p



+ 1113944mminus 1

j0u(k + j)

TRu(k + j)



J VTQV + U(k + m)

TRU(k + m) (47)


Q


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

R


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Φ

Ψ1Ψ2⋮Ψp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ψi

ρiδ 0 0 00 ρi

vrel0 0

0 0 ρia 0

0 0 0 ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(48)


J U(k + m)T

R + DTQD1113874 1113875U(k + m)

+ 21113882x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD1113883U(k + m)


the following form


Δx(k)gedc

vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(50)



U(k + m)leUmax


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(51)

where

M

dc

vmin

amin

jmin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

Inf

vmax

amax

jmax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L

1 0 0 0 00 1 0 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ptimesp

M

M

M

⋮M

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

N

N

⋮N

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umax

umax

⋮umax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umin

umin

⋮umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(52)


ΩU(k + m)leT (53)

where


T



Umax

minus Umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(54)




where

K R + DTQD

S x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD

(56)


6 Methods















1 50 10 15 22 30 15 10 2



amax 25ms2

umin minus 55ms2

umax 25ms2

jmin minus 3ms3

jmax 3ms3


Q diag 1 10 1 1

R 1p 10m 5


0

10

20

30

40

50

60

70

80Sp

acin

g (m

)

Time (s)



0 10 20 30 40 50

(a)

8

10

12

14

16

18

20

22

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash40

ndash20

0

20

40

60

80

100

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

0596

05965

0597

05975

0598

05985

0599

05995

06

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f)



Time (s)

0

10

20

30

40

50Sp

acin

g (m

)



0 10 20 30 40 50

(a)

8

9

10

11

12

13

14

15

16

17

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash30

ndash10

10

30

50

70

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

05975

05995

06015

06035

06055

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f )





8 Conclusion


Data Availability




Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018








ηm UcIc

Trebωm

(2)











Drivingdirection

Hydraulicbraking

Finaldrive

Transmission

Regenerativebraking

Motor ESP

Batte

ry p

ack

MCU

VCU

BMS

ACCcontroller

Brakingcontroller

Power system





Mot

or re

gene

rativ

ebr

akin

g to

rque

TMmax

ω0 ωini ωb ωend

Motor speed


Rint

Voc

ExternalLoading

Uc Ic




4 Lower Controller





z adec

g (6)

β Fbf

Fb

Fbf

Fbf + Fbr

(7)








Preset velocity







Own vehile state


Car-following plant


(i)(ii)

(i)(ii)

(i)(ii)

(a)(b)


(a)(b)

(ii)



(a)(b)

(i)(ii)



βgeb + zhg1113872 1113873

L 015le zle 08

βle(z + 004) b + zhg1113872 1113873

07zL 01le zle 052


07zL 01le zle 052

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)



Fbf Fb

Fbr 0(9)



07zL⎛⎝ ⎞⎠

Fbf Fb

(z + 004) l1 minus zhg1113872 1113873

07zL

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(10)



rw

Fbr Fb minus Fbf

(11)


Fbf Fbβ


5 Upper Controller







sf(k + 1) sf(k) + vf(k)Ts +12

af(k)T2s (15)

s(k + 1) s(k) + v(k)Ts +12

a(k)T2s (16)



vf(k + 1) vf(k) + af(k)Ts (17)

v(k + 1) v(k) + a(k)Ts (18)



1

3

4

Z1

Z2

Z3


Rear

axle

bra

king

forc

e (N

)

8000

7000

6000

5000

4000

3000

2000

1000

0




Δs(k + 1) sf(k + 1) minus s(k + 1) (19)




af(k)T2s minus

12

a(k)T2s

(21)




a(k + 1) 1 minusTs

τ1113874 1113875a(k) +

Ts

τu(k) (23)




Ts

(24)


j(k + 1) a(k + 1) minus a(k)

Ts

(25)


j(k + 1) minus1τ

a(k) +1τ

u(k) (26)




w(k) af(k) (28)


x(k + 1) Ax(k) + Bu(k) + Gw(k) (29)

where

A

1 0 Ts minus12T2s 0

0 1 0 Ts 0

0 0 1 minus Ts 0

0 0 0 1 minusTs

τ0

0 0 0 minus1τ

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B

0

0

0

Ts

τ

1τ

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

G

12T2s

0

Ts

0

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(30)









vrel(k)⟶ 0 as k⟶infin1113896 (33)



min |j(k)|1113896 (34)


y(k) δ(k) vrel(k) a(k) j(k)1113858 1113859T (35)



where

C

1 minus th 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

d0000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)





ρiδδ(k)


(38)



yr(k + i)

ρiδρi

vrel

ρia

ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦y(k) (39)











vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(42)





(44)


where

1113954Xp(k + p | k)

1113954xp(k + 1 | k)

1113954xp(k + 2 | k)

⋮

1113954xp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1113954Yp(k + p | k)

1113954yp(k + 1 | k)

1113954yp(k + 2 | k)

⋮

1113954yp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

U(k + m)

u(k)

u(k + 1)

⋮

u(k + m minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

W(k + p)

w(k)

w(k + 1)

⋮

w(k + p minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

A

A

A2

⋮

Ap

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B


AB B ⋱ 0

⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

G


AG G ⋱ ⋮

⋮ ⋮ ⋱ 0


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

C

CA

CA2

⋮

CAp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

D


CAB CB ⋱ 0

⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

E


CAG CG ⋱ ⋮

⋮ ⋮ ⋱ 0


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

Z

Z

⋮

Z

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)



J 1113944

p



+ 1113944mminus 1

j0u(k + j)

TRu(k + j)



J VTQV + U(k + m)

TRU(k + m) (47)


Q


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

R


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Φ

Ψ1Ψ2⋮Ψp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ψi

ρiδ 0 0 00 ρi

vrel0 0

0 0 ρia 0

0 0 0 ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(48)


J U(k + m)T

R + DTQD1113874 1113875U(k + m)

+ 21113882x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD1113883U(k + m)


the following form


Δx(k)gedc

vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(50)



U(k + m)leUmax


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(51)

where

M

dc

vmin

amin

jmin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

Inf

vmax

amax

jmax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L

1 0 0 0 00 1 0 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ptimesp

M

M

M

⋮M

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

N

N

⋮N

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umax

umax

⋮umax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umin

umin

⋮umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(52)


ΩU(k + m)leT (53)

where


T



Umax

minus Umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(54)




where

K R + DTQD

S x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD

(56)


6 Methods















1 50 10 15 22 30 15 10 2



amax 25ms2

umin minus 55ms2

umax 25ms2

jmin minus 3ms3

jmax 3ms3


Q diag 1 10 1 1

R 1p 10m 5


0

10

20

30

40

50

60

70

80Sp

acin

g (m

)

Time (s)



0 10 20 30 40 50

(a)

8

10

12

14

16

18

20

22

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash40

ndash20

0

20

40

60

80

100

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

0596

05965

0597

05975

0598

05985

0599

05995

06

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f)



Time (s)

0

10

20

30

40

50Sp

acin

g (m

)



0 10 20 30 40 50

(a)

8

9

10

11

12

13

14

15

16

17

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash30

ndash10

10

30

50

70

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

05975

05995

06015

06035

06055

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f )





8 Conclusion


Data Availability




Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018









4 Lower Controller





z adec

g (6)

β Fbf

Fb

Fbf

Fbf + Fbr

(7)








Preset velocity







Own vehile state


Car-following plant


(i)(ii)

(i)(ii)

(i)(ii)

(a)(b)


(a)(b)

(ii)



(a)(b)

(i)(ii)



βgeb + zhg1113872 1113873

L 015le zle 08

βle(z + 004) b + zhg1113872 1113873

07zL 01le zle 052


07zL 01le zle 052

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)



Fbf Fb

Fbr 0(9)



07zL⎛⎝ ⎞⎠

Fbf Fb

(z + 004) l1 minus zhg1113872 1113873

07zL

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(10)



rw

Fbr Fb minus Fbf

(11)


Fbf Fbβ


5 Upper Controller







sf(k + 1) sf(k) + vf(k)Ts +12

af(k)T2s (15)

s(k + 1) s(k) + v(k)Ts +12

a(k)T2s (16)



vf(k + 1) vf(k) + af(k)Ts (17)

v(k + 1) v(k) + a(k)Ts (18)



1

3

4

Z1

Z2

Z3


Rear

axle

bra

king

forc

e (N

)

8000

7000

6000

5000

4000

3000

2000

1000

0




Δs(k + 1) sf(k + 1) minus s(k + 1) (19)




af(k)T2s minus

12

a(k)T2s

(21)




a(k + 1) 1 minusTs

τ1113874 1113875a(k) +

Ts

τu(k) (23)




Ts

(24)


j(k + 1) a(k + 1) minus a(k)

Ts

(25)


j(k + 1) minus1τ

a(k) +1τ

u(k) (26)




w(k) af(k) (28)


x(k + 1) Ax(k) + Bu(k) + Gw(k) (29)

where

A

1 0 Ts minus12T2s 0

0 1 0 Ts 0

0 0 1 minus Ts 0

0 0 0 1 minusTs

τ0

0 0 0 minus1τ

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B

0

0

0

Ts

τ

1τ

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

G

12T2s

0

Ts

0

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(30)









vrel(k)⟶ 0 as k⟶infin1113896 (33)



min |j(k)|1113896 (34)


y(k) δ(k) vrel(k) a(k) j(k)1113858 1113859T (35)



where

C

1 minus th 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

d0000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)





ρiδδ(k)


(38)



yr(k + i)

ρiδρi

vrel

ρia

ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦y(k) (39)











vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(42)





(44)


where

1113954Xp(k + p | k)

1113954xp(k + 1 | k)

1113954xp(k + 2 | k)

⋮

1113954xp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1113954Yp(k + p | k)

1113954yp(k + 1 | k)

1113954yp(k + 2 | k)

⋮

1113954yp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

U(k + m)

u(k)

u(k + 1)

⋮

u(k + m minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

W(k + p)

w(k)

w(k + 1)

⋮

w(k + p minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

A

A

A2

⋮

Ap

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B


AB B ⋱ 0

⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

G


AG G ⋱ ⋮

⋮ ⋮ ⋱ 0


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

C

CA

CA2

⋮

CAp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

D


CAB CB ⋱ 0

⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

E


CAG CG ⋱ ⋮

⋮ ⋮ ⋱ 0


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

Z

Z

⋮

Z

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)



J 1113944

p



+ 1113944mminus 1

j0u(k + j)

TRu(k + j)



J VTQV + U(k + m)

TRU(k + m) (47)


Q


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

R


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Φ

Ψ1Ψ2⋮Ψp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ψi

ρiδ 0 0 00 ρi

vrel0 0

0 0 ρia 0

0 0 0 ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(48)


J U(k + m)T

R + DTQD1113874 1113875U(k + m)

+ 21113882x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD1113883U(k + m)


the following form


Δx(k)gedc

vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(50)



U(k + m)leUmax


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(51)

where

M

dc

vmin

amin

jmin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

Inf

vmax

amax

jmax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L

1 0 0 0 00 1 0 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ptimesp

M

M

M

⋮M

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

N

N

⋮N

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umax

umax

⋮umax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umin

umin

⋮umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(52)


ΩU(k + m)leT (53)

where


T



Umax

minus Umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(54)




where

K R + DTQD

S x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD

(56)


6 Methods















1 50 10 15 22 30 15 10 2



amax 25ms2

umin minus 55ms2

umax 25ms2

jmin minus 3ms3

jmax 3ms3


Q diag 1 10 1 1

R 1p 10m 5


0

10

20

30

40

50

60

70

80Sp

acin

g (m

)

Time (s)



0 10 20 30 40 50

(a)

8

10

12

14

16

18

20

22

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash40

ndash20

0

20

40

60

80

100

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

0596

05965

0597

05975

0598

05985

0599

05995

06

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f)



Time (s)

0

10

20

30

40

50Sp

acin

g (m

)



0 10 20 30 40 50

(a)

8

9

10

11

12

13

14

15

16

17

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash30

ndash10

10

30

50

70

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

05975

05995

06015

06035

06055

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f )





8 Conclusion


Data Availability




Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018








βgeb + zhg1113872 1113873

L 015le zle 08

βle(z + 004) b + zhg1113872 1113873

07zL 01le zle 052


07zL 01le zle 052

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)



Fbf Fb

Fbr 0(9)



07zL⎛⎝ ⎞⎠

Fbf Fb

(z + 004) l1 minus zhg1113872 1113873

07zL

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(10)



rw

Fbr Fb minus Fbf

(11)


Fbf Fbβ


5 Upper Controller







sf(k + 1) sf(k) + vf(k)Ts +12

af(k)T2s (15)

s(k + 1) s(k) + v(k)Ts +12

a(k)T2s (16)



vf(k + 1) vf(k) + af(k)Ts (17)

v(k + 1) v(k) + a(k)Ts (18)



1

3

4

Z1

Z2

Z3


Rear

axle

bra

king

forc

e (N

)

8000

7000

6000

5000

4000

3000

2000

1000

0




Δs(k + 1) sf(k + 1) minus s(k + 1) (19)




af(k)T2s minus

12

a(k)T2s

(21)




a(k + 1) 1 minusTs

τ1113874 1113875a(k) +

Ts

τu(k) (23)




Ts

(24)


j(k + 1) a(k + 1) minus a(k)

Ts

(25)


j(k + 1) minus1τ

a(k) +1τ

u(k) (26)




w(k) af(k) (28)


x(k + 1) Ax(k) + Bu(k) + Gw(k) (29)

where

A

1 0 Ts minus12T2s 0

0 1 0 Ts 0

0 0 1 minus Ts 0

0 0 0 1 minusTs

τ0

0 0 0 minus1τ

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B

0

0

0

Ts

τ

1τ

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

G

12T2s

0

Ts

0

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(30)









vrel(k)⟶ 0 as k⟶infin1113896 (33)



min |j(k)|1113896 (34)


y(k) δ(k) vrel(k) a(k) j(k)1113858 1113859T (35)



where

C

1 minus th 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

d0000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)





ρiδδ(k)


(38)



yr(k + i)

ρiδρi

vrel

ρia

ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦y(k) (39)











vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(42)





(44)


where

1113954Xp(k + p | k)

1113954xp(k + 1 | k)

1113954xp(k + 2 | k)

⋮

1113954xp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1113954Yp(k + p | k)

1113954yp(k + 1 | k)

1113954yp(k + 2 | k)

⋮

1113954yp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

U(k + m)

u(k)

u(k + 1)

⋮

u(k + m minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

W(k + p)

w(k)

w(k + 1)

⋮

w(k + p minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

A

A

A2

⋮

Ap

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B


AB B ⋱ 0

⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

G


AG G ⋱ ⋮

⋮ ⋮ ⋱ 0


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

C

CA

CA2

⋮

CAp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

D


CAB CB ⋱ 0

⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

E


CAG CG ⋱ ⋮

⋮ ⋮ ⋱ 0


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

Z

Z

⋮

Z

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)



J 1113944

p



+ 1113944mminus 1

j0u(k + j)

TRu(k + j)



J VTQV + U(k + m)

TRU(k + m) (47)


Q


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

R


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Φ

Ψ1Ψ2⋮Ψp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ψi

ρiδ 0 0 00 ρi

vrel0 0

0 0 ρia 0

0 0 0 ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(48)


J U(k + m)T

R + DTQD1113874 1113875U(k + m)

+ 21113882x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD1113883U(k + m)


the following form


Δx(k)gedc

vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(50)



U(k + m)leUmax


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(51)

where

M

dc

vmin

amin

jmin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

Inf

vmax

amax

jmax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L

1 0 0 0 00 1 0 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ptimesp

M

M

M

⋮M

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

N

N

⋮N

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umax

umax

⋮umax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umin

umin

⋮umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(52)


ΩU(k + m)leT (53)

where


T



Umax

minus Umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(54)




where

K R + DTQD

S x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD

(56)


6 Methods















1 50 10 15 22 30 15 10 2



amax 25ms2

umin minus 55ms2

umax 25ms2

jmin minus 3ms3

jmax 3ms3


Q diag 1 10 1 1

R 1p 10m 5


0

10

20

30

40

50

60

70

80Sp

acin

g (m

)

Time (s)



0 10 20 30 40 50

(a)

8

10

12

14

16

18

20

22

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash40

ndash20

0

20

40

60

80

100

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

0596

05965

0597

05975

0598

05985

0599

05995

06

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f)



Time (s)

0

10

20

30

40

50Sp

acin

g (m

)



0 10 20 30 40 50

(a)

8

9

10

11

12

13

14

15

16

17

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash30

ndash10

10

30

50

70

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

05975

05995

06015

06035

06055

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f )





8 Conclusion


Data Availability




Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018









Δs(k + 1) sf(k + 1) minus s(k + 1) (19)




af(k)T2s minus

12

a(k)T2s

(21)




a(k + 1) 1 minusTs

τ1113874 1113875a(k) +

Ts

τu(k) (23)




Ts

(24)


j(k + 1) a(k + 1) minus a(k)

Ts

(25)


j(k + 1) minus1τ

a(k) +1τ

u(k) (26)




w(k) af(k) (28)


x(k + 1) Ax(k) + Bu(k) + Gw(k) (29)

where

A

1 0 Ts minus12T2s 0

0 1 0 Ts 0

0 0 1 minus Ts 0

0 0 0 1 minusTs

τ0

0 0 0 minus1τ

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B

0

0

0

Ts

τ

1τ

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

G

12T2s

0

Ts

0

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(30)









vrel(k)⟶ 0 as k⟶infin1113896 (33)



min |j(k)|1113896 (34)


y(k) δ(k) vrel(k) a(k) j(k)1113858 1113859T (35)



where

C

1 minus th 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

d0000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)





ρiδδ(k)


(38)



yr(k + i)

ρiδρi

vrel

ρia

ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦y(k) (39)











vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(42)





(44)


where

1113954Xp(k + p | k)

1113954xp(k + 1 | k)

1113954xp(k + 2 | k)

⋮

1113954xp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1113954Yp(k + p | k)

1113954yp(k + 1 | k)

1113954yp(k + 2 | k)

⋮

1113954yp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

U(k + m)

u(k)

u(k + 1)

⋮

u(k + m minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

W(k + p)

w(k)

w(k + 1)

⋮

w(k + p minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

A

A

A2

⋮

Ap

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B


AB B ⋱ 0

⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

G


AG G ⋱ ⋮

⋮ ⋮ ⋱ 0


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

C

CA

CA2

⋮

CAp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

D


CAB CB ⋱ 0

⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

E


CAG CG ⋱ ⋮

⋮ ⋮ ⋱ 0


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

Z

Z

⋮

Z

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)



J 1113944

p



+ 1113944mminus 1

j0u(k + j)

TRu(k + j)



J VTQV + U(k + m)

TRU(k + m) (47)


Q


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

R


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Φ

Ψ1Ψ2⋮Ψp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ψi

ρiδ 0 0 00 ρi

vrel0 0

0 0 ρia 0

0 0 0 ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(48)


J U(k + m)T

R + DTQD1113874 1113875U(k + m)

+ 21113882x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD1113883U(k + m)


the following form


Δx(k)gedc

vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(50)



U(k + m)leUmax


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(51)

where

M

dc

vmin

amin

jmin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

Inf

vmax

amax

jmax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L

1 0 0 0 00 1 0 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ptimesp

M

M

M

⋮M

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

N

N

⋮N

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umax

umax

⋮umax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umin

umin

⋮umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(52)


ΩU(k + m)leT (53)

where


T



Umax

minus Umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(54)




where

K R + DTQD

S x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD

(56)


6 Methods















1 50 10 15 22 30 15 10 2



amax 25ms2

umin minus 55ms2

umax 25ms2

jmin minus 3ms3

jmax 3ms3


Q diag 1 10 1 1

R 1p 10m 5


0

10

20

30

40

50

60

70

80Sp

acin

g (m

)

Time (s)



0 10 20 30 40 50

(a)

8

10

12

14

16

18

20

22

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash40

ndash20

0

20

40

60

80

100

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

0596

05965

0597

05975

0598

05985

0599

05995

06

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f)



Time (s)

0

10

20

30

40

50Sp

acin

g (m

)



0 10 20 30 40 50

(a)

8

9

10

11

12

13

14

15

16

17

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash30

ndash10

10

30

50

70

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

05975

05995

06015

06035

06055

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f )





8 Conclusion


Data Availability




Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018













vrel(k)⟶ 0 as k⟶infin1113896 (33)



min |j(k)|1113896 (34)


y(k) δ(k) vrel(k) a(k) j(k)1113858 1113859T (35)



where

C

1 minus th 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

d0000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)





ρiδδ(k)


(38)



yr(k + i)

ρiδρi

vrel

ρia

ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦y(k) (39)











vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(42)





(44)


where

1113954Xp(k + p | k)

1113954xp(k + 1 | k)

1113954xp(k + 2 | k)

⋮

1113954xp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1113954Yp(k + p | k)

1113954yp(k + 1 | k)

1113954yp(k + 2 | k)

⋮

1113954yp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

U(k + m)

u(k)

u(k + 1)

⋮

u(k + m minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

W(k + p)

w(k)

w(k + 1)

⋮

w(k + p minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

A

A

A2

⋮

Ap

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B


AB B ⋱ 0

⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

G


AG G ⋱ ⋮

⋮ ⋮ ⋱ 0


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

C

CA

CA2

⋮

CAp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

D


CAB CB ⋱ 0

⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

E


CAG CG ⋱ ⋮

⋮ ⋮ ⋱ 0


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

Z

Z

⋮

Z

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)



J 1113944

p



+ 1113944mminus 1

j0u(k + j)

TRu(k + j)



J VTQV + U(k + m)

TRU(k + m) (47)


Q


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

R


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Φ

Ψ1Ψ2⋮Ψp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ψi

ρiδ 0 0 00 ρi

vrel0 0

0 0 ρia 0

0 0 0 ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(48)


J U(k + m)T

R + DTQD1113874 1113875U(k + m)

+ 21113882x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD1113883U(k + m)


the following form


Δx(k)gedc

vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(50)



U(k + m)leUmax


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(51)

where

M

dc

vmin

amin

jmin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

Inf

vmax

amax

jmax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L

1 0 0 0 00 1 0 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ptimesp

M

M

M

⋮M

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

N

N

⋮N

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umax

umax

⋮umax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umin

umin

⋮umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(52)


ΩU(k + m)leT (53)

where


T



Umax

minus Umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(54)




where

K R + DTQD

S x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD

(56)


6 Methods















1 50 10 15 22 30 15 10 2



amax 25ms2

umin minus 55ms2

umax 25ms2

jmin minus 3ms3

jmax 3ms3


Q diag 1 10 1 1

R 1p 10m 5


0

10

20

30

40

50

60

70

80Sp

acin

g (m

)

Time (s)



0 10 20 30 40 50

(a)

8

10

12

14

16

18

20

22

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash40

ndash20

0

20

40

60

80

100

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

0596

05965

0597

05975

0598

05985

0599

05995

06

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f)



Time (s)

0

10

20

30

40

50Sp

acin

g (m

)



0 10 20 30 40 50

(a)

8

9

10

11

12

13

14

15

16

17

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash30

ndash10

10

30

50

70

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

05975

05995

06015

06035

06055

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f )





8 Conclusion


Data Availability




Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018








where

1113954Xp(k + p | k)

1113954xp(k + 1 | k)

1113954xp(k + 2 | k)

⋮

1113954xp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1113954Yp(k + p | k)

1113954yp(k + 1 | k)

1113954yp(k + 2 | k)

⋮

1113954yp(k + p | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

U(k + m)

u(k)

u(k + 1)

⋮

u(k + m minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

W(k + p)

w(k)

w(k + 1)

⋮

w(k + p minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

A

A

A2

⋮

Ap

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

B


AB B ⋱ 0

⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

G


AG G ⋱ ⋮

⋮ ⋮ ⋱ 0


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

C

CA

CA2

⋮

CAp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

D


CAB CB ⋱ 0

⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

E


CAG CG ⋱ ⋮

⋮ ⋮ ⋱ 0


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Z

Z

Z

⋮

Z

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)



J 1113944

p



+ 1113944mminus 1

j0u(k + j)

TRu(k + j)



J VTQV + U(k + m)

TRU(k + m) (47)


Q


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

R


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Φ

Ψ1Ψ2⋮Ψp

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ψi

ρiδ 0 0 00 ρi

vrel0 0

0 0 ρia 0

0 0 0 ρij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(48)


J U(k + m)T

R + DTQD1113874 1113875U(k + m)

+ 21113882x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD1113883U(k + m)


the following form


Δx(k)gedc

vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(50)



U(k + m)leUmax


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(51)

where

M

dc

vmin

amin

jmin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

Inf

vmax

amax

jmax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L

1 0 0 0 00 1 0 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ptimesp

M

M

M

⋮M

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

N

N

⋮N

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umax

umax

⋮umax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umin

umin

⋮umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(52)


ΩU(k + m)leT (53)

where


T



Umax

minus Umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(54)




where

K R + DTQD

S x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD

(56)


6 Methods















1 50 10 15 22 30 15 10 2



amax 25ms2

umin minus 55ms2

umax 25ms2

jmin minus 3ms3

jmax 3ms3


Q diag 1 10 1 1

R 1p 10m 5


0

10

20

30

40

50

60

70

80Sp

acin

g (m

)

Time (s)



0 10 20 30 40 50

(a)

8

10

12

14

16

18

20

22

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash40

ndash20

0

20

40

60

80

100

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

0596

05965

0597

05975

0598

05985

0599

05995

06

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f)



Time (s)

0

10

20

30

40

50Sp

acin

g (m

)



0 10 20 30 40 50

(a)

8

9

10

11

12

13

14

15

16

17

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash30

ndash10

10

30

50

70

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

05975

05995

06015

06035

06055

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f )





8 Conclusion


Data Availability




Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018








Δx(k)gedc

vmin le v(k)le vmax

amin le a(k)le amax

jmin le j(k)le jmax

umin le u(k)le umax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(50)



U(k + m)leUmax


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(51)

where

M

dc

vmin

amin

jmin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

Inf

vmax

amax

jmax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L

1 0 0 0 00 1 0 0 00 0 0 1 00 0 0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

L


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ptimesp

M

M

M

⋮M

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N

N

N

⋮N

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umax

umax

⋮umax

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Umin

umin

⋮umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(52)


ΩU(k + m)leT (53)

where


T



Umax

minus Umin

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(54)




where

K R + DTQD

S x(k)T

CT

minus CTΦT

1113876 1113877QD + W(k + p)TE

TQD

minus ZT

minus ZTΦT

1113874 1113875QD

(56)


6 Methods















1 50 10 15 22 30 15 10 2



amax 25ms2

umin minus 55ms2

umax 25ms2

jmin minus 3ms3

jmax 3ms3


Q diag 1 10 1 1

R 1p 10m 5


0

10

20

30

40

50

60

70

80Sp

acin

g (m

)

Time (s)



0 10 20 30 40 50

(a)

8

10

12

14

16

18

20

22

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash40

ndash20

0

20

40

60

80

100

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

0596

05965

0597

05975

0598

05985

0599

05995

06

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f)



Time (s)

0

10

20

30

40

50Sp

acin

g (m

)



0 10 20 30 40 50

(a)

8

9

10

11

12

13

14

15

16

17

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash30

ndash10

10

30

50

70

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

05975

05995

06015

06035

06055

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f )





8 Conclusion


Data Availability




Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018



















1 50 10 15 22 30 15 10 2



amax 25ms2

umin minus 55ms2

umax 25ms2

jmin minus 3ms3

jmax 3ms3


Q diag 1 10 1 1

R 1p 10m 5


0

10

20

30

40

50

60

70

80Sp

acin

g (m

)

Time (s)



0 10 20 30 40 50

(a)

8

10

12

14

16

18

20

22

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash40

ndash20

0

20

40

60

80

100

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

0596

05965

0597

05975

0598

05985

0599

05995

06

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f)



Time (s)

0

10

20

30

40

50Sp

acin

g (m

)



0 10 20 30 40 50

(a)

8

9

10

11

12

13

14

15

16

17

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash30

ndash10

10

30

50

70

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

05975

05995

06015

06035

06055

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f )





8 Conclusion


Data Availability




Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018








0

10

20

30

40

50

60

70

80Sp

acin

g (m

)

Time (s)



0 10 20 30 40 50

(a)

8

10

12

14

16

18

20

22

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash40

ndash20

0

20

40

60

80

100

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

0596

05965

0597

05975

0598

05985

0599

05995

06

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f)



Time (s)

0

10

20

30

40

50Sp

acin

g (m

)



0 10 20 30 40 50

(a)

8

9

10

11

12

13

14

15

16

17

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash30

ndash10

10

30

50

70

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

05975

05995

06015

06035

06055

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f )





8 Conclusion


Data Availability




Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018








Time (s)

0

10

20

30

40

50Sp

acin

g (m

)



0 10 20 30 40 50

(a)

8

9

10

11

12

13

14

15

16

17

Spee

d (m

s)


Time (s)0 10 20 30 40 50

(b)

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

Acce

lera

tion

(ms

2 )


Time (s)0 10 20 30 40 50

(c)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20Je

rk (m

s3 )


Time (s)0 10 20 30 40 50

(d)

ndash30

ndash10

10

30

50

70

Batte

ry p

ower

(kW

)

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(e)

05955

05975

05995

06015

06035

06055

SOC

BER_CESTNO_ST

Time (s)0 10 20 30 40 50

(f )





8 Conclusion


Data Availability




Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018










8 Conclusion


Data Availability




Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018































Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








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