Adaptive, Nonlinear, And Learning Techniques for the Control of Vehicle Ride Dynamics

7/28/2019 Adaptive, Nonlinear, And Learning Techniques for the Control of Vehicle Ride Dynamics

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ADAPTIVE, NONLINEAR, AND

LEARNING TECHNIQUES FOR THECONTROL OF VEHICLE RIDE DYNAMICS

Timothy J. Gordon

Department of Aeronautical and Automotive Engineering

Loughborough University, United Kingdom

[email protected]

Abstract The ride dynamics of road vehicles is concerned with the control of

whole-body vibration, to provide comfort and vibration isolation for

occupants and transported goods. Ride isolation from road unevenness

is conventionally achieved through the pneumatic tire, coupled with

a spring and damper in the suspension; however substantial benefits

can be derived from active computer control of the suspension system.

Active ride control also benefits from on-line adaptation, and similar

advantage can be derived via nonlinear feedback control. This paper

reviews the fundamental issues and considers the potential for future

vehicles, against a background of increasing total system complexity and

interaction, as well as the continuing need for robust, safe, and fault-

tolerant operation. Consideration is also given to the use of intelligent

control systems that adapt and learn in real-time on the vehicle.

1. INTRODUCTION

The tire and suspension of a road vehicle provides an interface between

the vehicle structure and the road surface, to transmit forces for lateral

and longitudinal handling controlbraking, acceleration and cornering

and isolate road surface irregularities for vertical ride control. This

paper is concerned with the control of ride dynamics, wherein the prin-

cipal degrees of freedom are body-bounce, pitch, and roll, as well as

the relative motion of the wheels to the body. Assuming a rigid vehiclestructure, this corresponds to seven principal degrees of freedom for a

four-wheeled passenger vehicle. The ride control problem is to minimize

accelerations in the three body degrees of freedom, as well as control

body attitude (angular deflections) with respect to roll and pitch. This

is to be achieved for a large range of road conditions and vehicle speeds,

and working within the limited deflections available for both the suspen-

307

H. Aref and J.W. Philips (eds.), Mechanics for a New Millennium, 307326. 2001 Kluwer Academic Publishers. Printed in the Netherlands.


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308 EQ1SECTIONAL LECTURE : TIMOTHY J. GORDON

sion workspace and the tire structure. A further limitation derives from

the safety requirement that sufficient vertical tire loads are maintained,

in order to provide in-plane forces for cornering and braking.Active suspension control is achieved through some form of mechanicalactuationtypically a servo-hydraulic unit incorporating an electroni-

cally controlled spool valve to regulate hydraulic pressure, and hence

applied force or torque. The details of such actuators will not be con-sidered here; and while there are significant practical issues relating to

actuator technology, reliability and failure effects, cost, and power con-

sumption, it will be sufficient here to regard the suspension actuator

as a sub-system that can deliver force on demand. Also required is a

sensor set and a state observer (or equivalent signal processing) to recon-

struct real-time dynamic states from measured outputs. Again, we shall

assume this has been done, and the details will be skipped (see however

[1]).Although this paper has a specific focus on ride control, many of the

issues covered apply to a much wider class of dynamic control problems.

The general context includes adaptive vs. nonlinear control, effectiveness

of feed-forward information, intelligent and learning control, as well as

issues of dynamic system integration. In the next section, a review isundertaken of the main issues for automotive ride control. Section 3

considers some aspects of control system adaptation, which are taken

further in Section 4 in the form of on-line reinforcement learning. Opti-

mal nonlinear control techniques are then described in Section 5, andthe concluding section includes an outline of future research challenges.

2. OPTIMAL RIDE CONTROL

The quarter-car suspension model, shown in Fig. 1, has been usedwidely for fundamental investigations into ride control [2, 3, 4]. Thoughit contains just two of the seven ride degrees of freedom, it represents

much of the basic dynamics, and has proved particularly suitable for the

evaluation of fundamental control concepts. Vehicle parameters havebeen based on a medium-sized passenger car, and typical values may be

found in the cited references.For the standard passive system, the active force is zero, and there is

relatively limited scope for suspension tuning, at least within the contextof linear feedback and the quarter-car model. With the introduction of

computer controlled actuation, there is considerable scope for delivering

additional forces that might improve suspension performance in someway. The most direct way to optimize the ride performance of the sus-

pension is to use linear feedback of suspension states, via such optimal


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Control of vehicle ride dynamics 309

Figure 1 Quarter-car suspension model.

design methods as linear quadratic regulator (LQR) and Here

we focus on the simpler LQR method, where the time integral or sta-tistical expectation of a quadratic cost function is to be minimized, and

it can be rigorously shown that the closed-loop system gives minimumcost response to sudden events and Gaussian white noise inputs.

The cost function is commonly taken to be of the form

where T(t) is the dynamic vertical tire load, S(t) is the suspensionworkspace deflection, and A(t) is the vertical sprung mass (body) accel-

eration. The positive weighting parameters are adjustable to

suit the particular vehicle parameters and specific design requirements.Since it is only the ratio between these parameters that is significant, we

may set without any loss of generality. Parameters and maybe regarded as Lagrange multipliers, used to impose constraints on the

peak or RMS values ofTand S, under design conditions. In that case,the LQR optimal controller provides a rigorous minimum RMS value forA(t), or in other words gives a best comfort optimal controller.

Note that when Gaussian white noise is considered as an input forcontroller design, it is more for analytical convenience than for real-


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310 EQ1SECTIONAL LECTURE: TIMOTHY J. GORDON

world accuracy. However, the approximation is not unreasonable when

the model equations are expressed so that the dynamic input is the

vertical velocity v(t) of the roadtire interface.

The effectiveness of active control is indicated in Fig. 2, where fre-

quency response gains are shown for both active and passive suspension

systems. In each case v(t) is the input, and T(t), S(t), and A(t) arethe three outputs. Active 1 has been tuned against the passive sys-

Figure 2 Active and passive frequency response gains.

tem, to give identical peak tire load and suspension deflections under

design conditions, here prescribed as unit velocity initial conditions forthe unsprung and sprung masses respectively. For comparison, Active 2was allowed 25% more tire load variation and suspension deflection under

design conditions.

From the lower plot, both active systems enjoy substantially improved

ride isolation, compared with Passive, with the majority of improvement

being shown near the body bounce resonance frequency at approxi-

mately 1 Hz. Active 2 has the lowest body acceleration gain across

the whole frequency range, except for a single frequency, which coin-cides with the ideal wheel-hop resonance frequency for free vibration

of the unsprung mass on its tire spring. This is a particular example

of an invariant point, one of a small number that constrain dynamic


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responses in the quarter-car system; all active and passive suspensionsystem variants have coincident gains at such specific frequencies [6].

The frequency responses in the upper two plots, for the constraintvariables, show that Active 1 is always at least comparable with Passive,

with the exception of increased suspension gain at low frequencies, afeature that is described further below. Active 2 on the other hand allowsgreatly increased wheel motion at the wheel-hop resonance, giving rise to

increased dynamic tire loads and suspension variations at this frequency.

However, it is fundamental to what follows to note that this is not always

detrimental to system performance; provided the excitation amplitude

at these frequencies is sufficiently low, Active 2 can usefully improve ride

comfort isolation compared with Passive and Active 1.While the active suspension is an interesting concept for dynamic

control, it may not always be considered feasible, due to practical con-

siderations of weight, packaging, cost, and power consumption. In this

case, an interesting alternative is the semi-active suspension, which is

designed to modulate the dissipation of energy from the suspension, but

without any external source of mechanical power [7]. One way this canbe achieved is via an electronically controlled spool valve within an oth-

erwise standard hydraulic damper; provided the valve has sufficientlyfast transient response, and the range of damping rates is sufficiently

large, the semi-active system performance can theoretically approachthat of the active suspension. This is demonstrated in Fig. 3, where

three road bumps generate significant disturbance for the passive sys-

tem, while active and semi-active both filter the input approximately

equally. The semi-active model is very much idealized (though so is

the active system), but the conclusion that a well designed semi-active

system can produce significant ride benefits is certainly valid.An interesting problem for active suspensions arises through the use

of skyhook damping. In the LQR active control, all available sus-

pension states are fed back into the actuator, including the absolute

vertical body velocityi.e. the velocity of the sprung mass relative to

the original rest frame. In fact, without such skyhook damping, the ridecontrol system reverts to something very similar to a standard passive

suspension, and therefore its use is particularly significant. The problem

alluded to occurs whenever the active suspension vehicle ascends a road

of constant incline; this induces a steady-state velocity that feeds backa non-zero signal to the actuator. This results in a steady-state suspen-

sion offset, where the suspension spring force (including any suspension

deflection feedback gain in the active control law) cancels the erroneous

skyhook damping force. The problem is also apparent from the nonzero

suspension gain at 0 Hz shown in Fig. 2. It can be solved in a number


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Figure 3 Comparison of passive, active and semi-active systems.

of ad hoc ways, but is fundamentally due to an incomplete description ofthe road surface geometry in the underlying optimal design. The incom-pleteness relates to low frequencies generally, not just to steady-state,and a systematic solution to this problem requires a subtle modificationto the control optimization [8].

3. ADAPTATION OF RIDE CONTROLFEEDBACK

It is apparent from Fig. 2 that there is a compromise, or trade-off,between tire and suspension deflections on the one hand, and ride com-fort on the other. When the road input amplitude is large, there isdanger of exceeding available suspension workspace limits, or of losingcontact between the tire and road surface; in this case ride comfort must

be sacrificed for the suspension, and hence the vehicle, to operate safely.At lower amplitudes, where such limits are not an issue, it is desirableto soften the active suspension and improve ride comfort. To achievethis, some form of on-line adaptation is necessary. Conceptually, thesimplest approach is gain scheduling; a set of LQR gains are designedoff-line to accommodate the various expected road inputs types (vary-ing with amplitude and frequency content), and as different conditions


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Figure 4 Control of vertical tire load for severe events.

are experienced, the vehicle response is used to estimate best-fit design

conditions, and hence adapt controller gains [9].

Table 1 Test road profile component events (at 15 m/s)

Figures 4 and 5 show suspension responses to an aggressive test road

profile that consists of a series of raised sinusoidal bumps and linearinclinesone large one up, followed by four shorter ones downsee

Table 1. The road speed is a moderate 15 m/s, but gives rise to severe


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Figure 5 Control of suspension workspace.

vertical inputs, as can be seen from the Passive responses in the follow-

ing plots. Figure 4 shows vertical tire loads for Passive, Active 1, andActive 2, as well as a further Adaptive system. These tire loads now

include the static component, and should therefore remain well above

zero for safe handling control. Clearly this is far from the case for Pas-

sive; and while the Active systems are greatly improved, the Adaptive

system provides a much better and consistent minimum load across thevarious surface changes.

In Fig. 5, unconstrained suspension travel is shown, even though a

real vehicle is always subject to workspace limits. For a medium-sized

passenger vehicle, workspace of around 0.1 m would be typical, or even

generous, and it is clear that the non-adaptive systems all exceed this

limit on occasion. In reality, a suspension will include bump rubbers to

reduce the worst effects of metal-on-metal contact, but it is reasonable

to expect an active suspension to be designed to control such events asfar as possible, and it clear that the adaptive system is superior in thisaspect.

An important point here is that an adaptive suspension of this type

combines the above authority over tire load and workspace, with highlevels of ride comfort wherever this is possible. Figure 6 shows thecorresponding vertical body accelerations, where Passive gives relatively


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Figure 6 Vertical body accelerations.

poor ride comfort whenever the road generates significant amounts ofbody bounceon the initial set of bumps, and on the later ramp eventsthough between t = 6 s and 15 s, where the input frequencies are higher,

the passive ride is comparatively reasonable. Overall, the ride comfortpredicted for Active 1 is much improved over Passive; on the other hand,

Active 2 is too good to be true, because the system design has sacrificed

suspension and tire load control for the apparent improvement in ridecomfort. For example, for 15 s < t < 15.5 s, the ramp induces very little

body acceleration, but there is very large suspension compression, asseen in Fig. 5. A more reasonable comparison can be made between

Adaptive and Active 1, where it is clear that Adaptive gives equal or

lower accelerations, except where the need to meet tire or suspension

constraints leads to higher suspension forces, and hence higher body

accelerations.

In terms of real-time application, there are a number of remainingissues. The adaptation implemented here is based on a full knowledge

of the road profile, where in reality the system must adapt as a function

of vehicle response. For example, the sudden events occurring between19 s and 23 s on the above plots, which cause poor tire load control for

the other systems, each require an adaptive switch to hard response tooccur within around 20 ms. A second issue relates to the integration with


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handling dynamic control, which is important at low lateral accelerations

on smooth roads; a very soft suspension provides poor control of body

motion, and also poor feedback to the driver. Both of these aspects aretaken up later.

4. LEARNING CONTROL

An alternative approach to control system design and adaptation isvia reinforcement learning. Such an approach uses a computer system toact on the dynamic controller, and adapt the operation of the controller

to reinforce desirable closed-loop performance. As with traditional adap-

Figure 7 System architecture for the CARLA learning process.

tive control, reinforcement learning must operate on a slower timescale

than the underlying system dynamics, and normally the timescale is

very much slower. The simplest such approach is non-associative rein-

forcement learning, where the learning system treats the controller and

vehicle as a black box, and applies actions by setting control parame-

ters.

Recent work on the application of reinforcement learning to ride con-trol has used stochastic learning automata in both simulation and real-

time practical implementation [10, 11, 12]. An effective approach hasbeen to employ a team of Continuous Action Reinforcement Learn-ing Automata (CARLA) [13]. Each CARLA defines an action based onprobability densities, and in this case each action corresponds to defininga control system parameter, such as a feedback gain (Fig. 7).


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At each iteration n, the ith CARLA has an associated probability

density where is the corresponding control parameter with

a pre-defined range Using a pseudo-random number generatorwith uniformly distributed variate, is selected and usedto define according to the formula

The full set of control parameters are then implemented, in real time

or in simulation, to control the vehicle dynamics for a pre-assigned period

of time, and then a cost function, possibly similar to that of Eqn. (1),is used to assess performance cost J(n) and define a reward signalA rewardinaction reinforcement algorithm alters the set of probabilitydensity functions whenever improved performance is achieved, and nochange is made otherwise. The reward and probability update equationsare

where and are respectively the median and minimumcost values measured during the previous m samples, is a scale fac-tor, defined to normalize to unit area within and

is a symmetric Gaussian neighborhood function, which diffuses

the reinforcement of probability over neighboring values of the controller

gain

The CARLA approach has been applied to a variety of simulation andreal-world control problems. In the simulation of a fully active suspen-

sion control system, the method reproduces optimal LQR gains with

minimal errors. However, being much less limited in its underlyingmathematical assumptions, the CARLA approach can successfully opti-

mize controller gains for more general conditions than are possible withLQRfor example, the learning system can directly use real or realistic

road surface data in place of Gaussian white noise [12].

Figure 8 shows a typical probability density function, created duringreal vehicle learning of a semi-active controller; in this case the learning

took place using stationary random disturbances from a four-poster road

simulator rig. In the figure, the sharp peak created at around = 1000


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Figure 8 Probability density convergence for semi-active ride control.

corresponds to a preferred suspension spring stiffness gain of around 50%of the existing passive value on the vehicle.

Thus improved control results from the passive suspension force can-

celling 50% of the spring force whenever energy considerations makethis possible. Furthermore, this result does not depend on any model-

ing assumptions, since it was derived from the actual vehicle test; the

approach thus provides a valuable diagnostic tool, as well as providingan optimal controller.

It is worth noting that learning on real roads is a much more chal-

lenging exercise, due to the nonstationary nature of the input, and while

some progress has been made to achieve satisfactory learning and adap-tation, further work remains to be done.

5. NONLINEAR OPTIMAL CONTROL

There are many situations where nonlinear control techniques may

be preferred over linear methods, though there are often serious tech-

nical difficulties associated with achievingor even definingthe bestnonlinear control for any given problem. Particular cases are when the

underlying system model is taken to be nonlinear [14, 15] or when the

control objectives naturally lead to nonlinearity [16, 17]. For ride con-trol, the former category includes the application of semi-active or other

force-limited actuation, while the latter includes the imposition of fixed

limits on suspension workspace and absolute criteria for vertical tire loadcontrol. The use of gain scheduling and other forms of adaptive controlis essentially a heuristic approach, used in the absence of more powerfulnonlinear control design methods.


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Nonlinear optimal control (NOC) is a well-known concept that is

under-used, mainly because implementation is often impractical. The

results described below are obtained using the famous Pontryagin max-imum principle, via numerical techniques outlined in [15, 17]; the

approach is computationally intensive and is not suitable for real-time

application. And while neural networks offer new opportunities forreal-time application of NOC, the underlying curse of dimensionality

remainsfor anything other than low-order systems, large amounts of

information must be encoded into the neural network, and excessive

training times may result. However, NOC offers interesting opportuni-

ties for investigating the theoretical limits of a control system, and hence

provides a benchmark for more practical control schemes; here we shall

use this approach to assess the active suspension results obtained above.

For demonstration, we modify the control objectives, but retain an

underlying linear description of the suspension. The dynamic cost for

suspension workspace is modified to impose rigid limits at with

a = 100 mm in simulation. A term

is added to the cost function (1)with Active 2 parametersand clearly

as To improve the tire load control ofActive 2, a fur-

ther term is also added that becomes significant only for large dynamic

tire load variations:

The resulting suspension and tire components of the cost function

(including quadratic terms from Eqn. (1)) are shown in Fig. 9. Theresulting dynamic responses on the test road surface are shown in Fig. 10,where the nonlinear results are referred to as NOC, and again compar-isons are made using Active 1 as a reference. Overall, as expected, theNOCsuspension workspace is rigorously maintained within the available

limits. There is a single event at t = 15.5 s, at the end of the upward

ramp, where NOC tire load is controlled less effectively, but it is easyto understand why. Active 1 exceeds the suspension constraint at this

point, in an effort to hold the tire on the road surface; this is simply notpossible, and the NOCresults reflect this. Elsewhere (e.g. 6 s < t < 10 s)

NOCmaintains somewhat better tire load control, and where constraints

are unimportant (e.g. 10 s < t < 15 s) the body acceleration for NOC

is also improved. Thus NOCshares all of the benefits of the previous

Adaptive control, but without the associated difficulties of detection andinference.


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Figure 9 Modified cost functions for tire load and suspension workspace.

An interesting result arises from the ability of nonlinear optimal con-

trol to exploit a wide range of cost function modifications. The reader

may have noticed an anomaly, that the above cost functionswhether

quadratic or more generalhave been chosen symmetrical with respect

to both tire load T and suspension deflection S. While this is certainly

sensible for S, it is clear that only reductions in tire load cause con-

cern for handling control, and therefore in place of Eqn. (1) we mightsubstitute the following:

Simulations show that, provided the value of is doubled from the

previous value (to reflect the fact that it is used only half of the time)

the dynamic responses are virtually identical to the previous linear sys-

tem.Far more significant is the effect of using previewed (or look-ahead)information from the road surface. Although this has already been

included in a very simple manner for the Adaptive system, there aregreat potential benefits when such information is available as a dynamic

input to the controller [4, 15, 18, 19]. Again both linear and nonlin-ear approaches are available, though linear methods are not valid for


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Figure 10 Comparison of NOC with linear Active 1 responses.

semi-active suspension, or other conditions where the underlying modelis nonlinear, or where as above the control objectives force the non-

linearity. Figure 11 compares the previous NOC results with the casewhere accurate one-second preview is available. Here the improvementin body acceleration is impressive and overwhelmingthe active sus-

pension makes effective use of available suspension workspace and tireload variations, without losing control, and to effect excellent ride vibra-

tion isolation. Of course there are questions over the degradation of

such results due to modeling errors, sensor type, and accuracy, and over

signal processing requirements for preview-based control; but the factremains that ride isolation is very sensitive to the addition of such infor-mation, and even imperfect preview is potentially effective. For example,

in [18] a linear analysis shows that rear suspension response may be sig-

nificantly improved by feeding forward the dynamic responses from the

front wheels.

6. CONCLUSIONS

The above work has addressed a number of fundamental issues con-cerned with the ride dynamics of road vehicles. The literature on thesubject is vast, and the references given here provide only a sampled


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Figure 11 Inclusion of preview information for NOC.

introduction. Many of the issues are well known, though the results pre-

sented here on nonlinear optimal control are new. In this short paper itis not possible to go very far into the issues that lie beyond the quarter-

car concept, and indeed much of the literature is also restricted to this

simple model. However, in conclusion is seems appropriate to consider

current and future research issues involving ride dynamics, and these

very definitely go beyond such a limited perspective, and involve inter-actions with handling, safety, and driver information systemsin other

words, are concerned with dynamic systems integration.

In its simplest practical form, systems integration means increasing

the use of common hardware, sensors, communication, and data analysis

within the vehicle environment, on the basis that duplication is waste-

ful. A more fundamental aspect of dynamic systems integration is tobalance design objectives for various systems, so that interactions and

compromises (e.g. between ride and handling) are properly addressedat the design stage. This is essentially the application of multivariable

control to a large and complex systemthe vehicleso that multiple

objectives can be optimized in a systematic and simultaneous fashion.Unfortunately, a global system approach to vehicle dynamics control

is not necessarily practical or even desirable. A basic problem is that

vehicle manufacturers and systems suppliers are often not the same com-


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panies, so that complete sharing of design knowledgeespecially controlalgorithmssimply does not occur. Control algorithms are often embed-

ded as black boxes, and a systems supplier is more likely to tune thesystem to the vehicle rather than share details of embedded algorithms

with the vehicle manufacturer or other systems suppliers. Although this

is only a commercial problem, it is a very real one, and is associated

with a more fundamental problem of vehiclesystem combinatorics; asnew vehicles and systems are developed, between various different com-

panies, each offering several different options to customers, the num-

ber of distinct vehicle variants grows factorially, and it becomes totally

unreasonable to design separate software for every such combination.

Also, as vehicles and their control systems become increasingly com-plex, there is less scope for providing underlying mathematical models

for the total system behavior; and where such models do exist, they are

limited by the need for linearity in most existing multivariable controlmethods.

Thus the expected trend for dynamic systems integration on road vehi-

cles is for more intensive real-time computation and on-line optimiza-

tion, more intelligence and learning within the vehicle systems, more

parallelism and modularity in design, and for the integration (includ-ing trade-offs and compromises) to actually take place dynamically on

the vehicle. Some small progress in this direction has been reported

by the author [20, 22] but it is clear that new techniques are required.

The work presented here suggests that a minimum requirement for such

dynamic integration is that it should include scope for nonlinear behav-

ior, and make use of adaptation and learning in the real-world oper-ating environment. A further key requirement, that potentially comes

for free, is that of robust and fault-tolerant operation; dynamic inte-gration and optimization in real time can also accommodate dynamic

re-optimization once localized failures are detected [20, 21]. Finallythere must be suitable interfaces with the driver and passengersso

that individual preferences and driving styles are taken into account in

the dynamic integration process. These future challenges are immense,

but also immensely exciting.

References

[1] Best, M. C. 1995. On the modelling requirements for the practical implementa-

tion of advanced vehicle suspension control, Ph.D. Thesis, Loughborough Uni-

versity.

[2] Thompson, A. G. 1970. Design of active suspensions. Proceedings of the Insti-

tution of Mechanical Engineers (Part I) 185, 553563.


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[3] Thompson, A. G. 1976. Active suspensions with optimal linear state feedback.Vehicle System Dynamics 5, 187203.

[4] Hac, A. 1992. Optimal linear preview control of active vehicle suspension. Vehicle

System Dynamics 21, 167195.

[5] Yamashita, M., K. Fujimori, C. Uhlik, R. Kawatani, and H. Kimura. 1990.

control of an automotive active suspension. Proceedings of the 29th Conference

on Decision and Control, 22442250.

[6] Hedrik, J. K., and T. Butsuen. 1988. Invariant properties of automotive sus-pensions. Proceedings of the Institution of Mechanical Engineers International

Conference on Advanced Suspensions, London.

[7] Margolis, D. L. 1982. Semi-active heave and pitch control for ground vehicles.

Vehicle System Dynamics 11, 3142.[8] Fairgrieve, A., and T. J. Gordon. 2000. On-line estimation of local road gradient

for improved steady-state suspension deflection control. Vehicle System Dynam-ics 33 (SupplementDynamics of Vehicles on Roads and Tracks), 590603.

[9] ElBeheiry, E. M., and D. C. Karnopp. 1996. Optimal control of vehicle random

vibration with constrained suspension deflection. Journal of Sound and Vibra-

tion 189, 547564.

[10] Gordon, T. J., C. Marsh, and Q. H. Wu. 1993. Stochastic optimal control of

active vehicle suspensions using learning automata. Proceedings of the Institu-

tion of Mechanical EngineersPart I (Journal of Systems and Control Engi-neering) 207, 143152.

[11] Marsh, C., T. J. Gordon, and Q. H. Wu. 1995. The application of learning

automata to controller design in slow-active automotive suspensions. Vehicle

System Dynamics 24, 597616.

[12] Frost, G. P., T. J. Gordon, M. N. Howell, and Q. H. Wu. 1996. Moderated

reinforcement learning of active and semi-active vehicle suspension control laws.Proceedings of the Institution of Mechanical EngineersPart I (Journal of Sys-

tems and Control Engineering) 210, 249257.

[13] Howell, M. N., G. P. Frost, T. J. Gordon, and Q. H. Wu. 1997. Continuous actionreinforcement learning applied to vehicle suspension control. Mechatronics 7,263276.

[14] Ono, E., S. Hosoe, H. D. Tuan, and Y. Hayashi. 1996. Nonlinear control

of active suspension. Vehicle System Dynamics 25 (SupplementDynamics ofVehicles on Roads and Tracks), 489401.

[15] Gordon, T. J., and R. S. Sharp. 1998. On improving the performance of auto-motive semi-active suspension systems through road preview. Journal of Sound

and Vibration 217 , 163182.

[16] Gordon, T. J., C. Marsh, and M. G. Milsted. 1991. A comparison of adaptive

LQG and nonlinear controllers for vehicle suspension systems. Vehicle SystemDynamics 20, 321340.

[17] Gordon, T. J., and M. C. Best. 1994. Dynamic optimization of nonlinear semi-

active suspension controllers. Proceedings of the Institution of Electrical Engi-

neers (IEE) 1994 International Conference Control 94 (IEE Publication no.

389), Warwick, U.K., 332337.


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[18] Sharp, R. S., and D. A. Wilson. 1990. On control laws for vehicle suspensions

accounting for input correlations. Vehicle System Dynamics 19, 353363.

[19] Louam, N., D. A. Wilson, and R. S. Sharp. Optimization and performanceenhancement of active suspensions for automobiles under preview of the road.

Vehicle System Dynamics 21, 3963.

[20] Gordon, T. J. 1995. An integrated strategy for the control of complex mechanical

systems based on sub-system optimality criteria. Proceedings of the IUTAM

Symposium on Optimization of Mechanical Systems (Stuttgart, 1995) (D. Bestle

and W. Schiehlen, eds.). Dordrecht: Kluwer, 97104.

[21] Gordon, T. J. 1996. An integrated strategy for the control of a full vehicle active

suspension system. Vehicle System Dynamics 25 (SupplementDynamics of

Vehicles on Roads and Tracks), 229242.

[22] Frost, G. P., M. N. Howell, T. J. Gordon, and Q. H. Wu. 1996. Dynamic vehi-

cle roll control using reinforcement learning. Proceedings of the 1996 United

Kingdom Automatic Control Council International Conference on CONTROL

96 (Exeter, U.K.), 11071118.


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ICTAM 2000 participants line up at one of several carving tables at the Welcome

Reception on Monday evening, 28 August 2000. University of Illinois president

James J. Stukel hosted the event.

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Adaptive, Nonlinear, And Learning Techniques for the Control of Vehicle Ride Dynamics