872 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 3, MAY 2004

Control of a Parallel Hybrid Powertrain:Optimal Control

Sebastien Delprat, Jimmy Lauber, Thierry Marie Guerra, and J. Rimaux

Abstract—Control strategies for hybrid powertrains are algo-rithms that choose the power split between the engine and motor ofa hybrid vehicle in order to minimize the fuel consumption and/oremissions. The goal of this paper is to propose an efficient tool toevaluate minimal fuel consumption that is achievable in simulation.Several approaches have been proposed, using heuristics (Delpratet al. 1999) or dynamic programming (Brahma et al., 2000; Rimauxet al., 1999). One drawback of these approaches is the huge amountof time required to obtain solutions. The approach described hereis based on optimal control theory (Lewis & Syrmos, 1995) andavoids this drawback. Moreover, it can be easily applied to a largefamily of parallel arrangements.

Index Terms—Control strategy, hybrid vehicle, optimal control.

NOMENCLATURE

Sample, .Sampling time.

• VehicleWheel speed (rpm).Torque at the wheel (Nm).

• GearboxGear number.At a given sample, set of admissible gearnumber, i.e., with two gears: {{1}, {2}, {1,2}}.Reduction ratio for the th gear.Gearbox efficiency.

• Reduction gearsReduction ratio.Reduction gears efficiency.

• IC engineSpeed (rpm).Torque at output shaft (Nm).

, Minimal and maximal speed (rpm).

Maximal torque at speed (Nm).

Manuscript received April 26, 2002; revised December 20, 2002, September1, 2003, and November 20, 2003. This work is the result of a collaborationbetween the Laboratoire d’Automatique, de Mécanique et d’Informatique In-dustrielles et Humaines, Valenciennes, France (LAMIH) and PSA Peugeot Cit-roën, Vélizy Villacoublay Cedex, France, and has been supported by the Agencede l’Environnement et de la Maîtrise de l’énergie (ADEME) and the Fond Eu-ropéen pour le DÉveloppement Régional (FEDER).

S. Delprat, J. Lauber, and T. M. Guerra are with the Université de Valenci-ennes et du Hainaut Cambrésis, Le Mont Houy Cedex 59300, France (e-mail:delprat@univ-valenciennes.fr; lauber@univ-valenciennes.fr; guerra@univ-va-lenciennes.fr).

J. Rimaux is with PSA Peugeot Citroën, Vélizy Villacoublay Cedex 78943,France (e-mail: Janette.Rimaux@mpsa.com).

Digital Object Identifier 10.1109/TVT.2004.827161

Fuel consumption required producing thetorque at speed (gr/s).The same according to the decision vari-ables and (gr/s).

• Electric motorSpeed (rpm).Torque (Nm).Maximum speed (rpm).Minimum torque at speed (Nm).Maximum torque at speed (Nm).Power (including all losses) required pro-ducing the torque at speed(W).The same written according to the decisionvariables and (W).Power (without battery losses) requiredproducing the torque at speed(W).The same written according to the decisionvariables and (W).

• BatteryState of charge.Charge acceptance, i.e., battery efficiency.The same written according to the decisionvariables and .Overall battery state of charge variationover a speed cycle.

I. INTRODUCTION

HYBRID vehicles use at least two energy sources fortheir propelling; usually, an electric motor is associated

with an internal combustion (IC) engine. The motor providesthe ability to recover kinetic energy during braking phases,whereas the engine ensures a range similar to a conventionalvehicle. In comparison with a conventional car, the goals areto reduce emissions and fuel consumption in a significant way.To achieve these goals, several ways can be investigated in thefield of engineering. For example, reducing the vehicle weight,improving the IC engine control, designing more efficientmechanical parts, and so on. Among all these possibilities, wewill suppose that all the components (motor, IC engine, battery,car, etc.) to be fixed and we investigate how to manage theenergy flows in the powertrain. In other words, an arrangementbeing chosen, what is the “best” control strategy?

We can distinguish two classes of algorithms. The first con-cerns a real-time control strategy that can be used to control avehicle. Several algorithms have been proposed, some of which

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DELPRAT et al.: CONTROL OF A PARALLEL HYBRID POWERTRAIN 873

use fuzzy logiccontrollers [3], [4] and others are based on anenergy-flow analysis [5], [6].

A second-class of algorithms deals with global optimization insimulation. In this case, the vehicle speed is regulated to follow aspeed cycle using a torque at the wheel controller. A first objec-tive is to compute the minimum fuel consumption that is achiev-able with a given prototype on a given speed cycle. Several algo-rithms have been proposed to solve this problem; for example,simulated annealing [7] or algorithms based on dynamic pro-gramming [8], [9]. These algorithms require a lot of computa-tional time and a fine tuning of their parameters and their use isthen restricted to short speed cycles and single experiments. Tooutperform these algorithms, another efficient approach basedon the optimal control theory is proposed. It allows very fast re-sults to be obtained and can be used for another purpose. Ac-cording to the fact that, for the model and the criterion taken intoaccount, optimal results are obtained and. thus, we have got thelower bound of consumption for a given cycle. Therefore, thisalgorithm is used to evaluate all the other kinds of control strate-gies, especially those dedicated to real-time control.

The paper is organized as follows. In the first part, the dif-ferent powertrain modeling used for simulation and the controlare presented. Parts two and three describe the optimal con-trol theory applied to such arrangements via different batterymodels. At last, some results for a prototype built at the LAMIHare presented.

II. HYBRID VEHICLE MODELING

For this study, two levels of modeling are considered. Thefirst, called model 1, is used to simulate the vehicle over speedcycles. It represents only the longitudinal behavior and is de-signed for the energetic-consumption simulation. It includes thefollowing:

• dynamic behavior on the IC engine torque;• model of the motor based on physical equations (magnetic

saturation, electric relations, etc.);• full dynamic vehicle model (aerodynamics, nonlinear tires

friction, etc.);• battery model based on the charge acceptance [11].

An important part of model 1 is the IC engine modeling. Thisis done only for fuel consumption using classical maps and isvalidated according to real data results.

Based on this first model, a simplified model, called model 2,has been derived to allow a “nice” formulation of the optimiza-tion problem and, moreover, a “nice” way to solve it. In thissimplified model, the IC engine dynamics are neglected and theelectric drive (motor + battery) model is based on maps.

The purpose of this paper is not the vehicle modeling, butcontrol law synthesis. So only model 2 is presented as this modelis used to derive the optimization algorithm. Model 1 is omittedhere (the reader can refer to [12] for explanations), but model 1is used for the simulation results at the end of this paper.

A. Energetic-Consumption Modeling (Model 2)

The battery is considered as a dynamical system, with thestate of charge

(1)

represents the power required (includingbattery losses) to produce the torque at speed . With

, the instantaneous fuel consumption of the ICengine required to produce the torque at speed , thetotal fuel consumption over samples is

(2)

and are represented by data maps over speed andtorque. The proposed methodology is generic in the sense thatit depends only on the data given by maps, i.e., it can be easilyused for other motors and engines.

B. Mechanical Constraints

The speeds and torques of both the engine and motor are lim-ited by the following mechanical constraints.

• Constraints on speeds

(3)

(4)

• Constraints on torques

(5)

(6)

C. Mechanical Arrangement and Decision Variables

The presented algorithm has been developed for paralleltorque-addition arrangements; for example, the parallel single-or double-shaft arrangement or small hybrid vehicles with analterno-starter. Extensions to some other arrangements (powersplit and serial arrangement) are easy to do under some minorchanges.

Parallel Single-Shaft Arrangements: In the parallel single-shaft arrangement Fig. 1(a), both the engine and motor use thesame shaft. If the motor is not powerful enough to propel thevehicle alone (i.e., alterno-starter), it may be located betweenthe engine and the clutch. Another variation is to add a set ofreduction gears to ensure that both the engine and motor achievetheir maximal speed simultaneously between the motor and theengine [Fig. 1(b)].

Two main relations describe the parallel single-shaft arrange-ment shown in Fig. 1(b), as follows:

• speed relation

(7)

• torque relation

(8)

Remark: with , (7) and (8) provide relations for the ar-rangement, shown in Fig. 1(a).

According to (7), the ratio between the engine and motorspeed is constant due to the single-shaft arrangement. This ar-rangement is said to be “torque addition” because the torque at

874 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 3, MAY 2004

(a)

(b)

Fig. 1.(a) Parallel single-shaft arrangement. (b) Parallel single shaft with areductor.

Fig. 2. Parallel double-shaft arrangement.

the wheel is proportional to the sum of the engine and motortorques (8).

Parallel Double-Shaft Arrangement: In this arrangement(Fig. 2), the engine and motor have separated shafts. Accordingto the mechanical arrangement, the following expressions areobtained:

(9)

(10)

Clearly, being fixed by design, according to (9) the ratio be-tween the engine and motor speeds depends only on the chosengear number .

D. Toward a Generic Optimization Problem

Let us recall that the torque at the wheel and the vehiclespeed are known and given by a speed cycle. It is obviousthat the whole powertrain set point can be defined using only

two decision variables: one torque (the IC engine torquein the following) and the gear number . Moreover, a uniqueexpression for the energetic-consumption model and speed andtorque constraints can be obtained, regardless to the mechanicalarrangement. Thus, a unique optimization problem can be for-mulated, as well as a unique algorithm for several arrangements.

The relationships between the decision variables and the dif-ferent torques and speeds, (7) and (8) or (9) and (10), allowwriting the constraints (5) and (6) as

(11)

For a given gear number , anddefine the interval of admissible values

for IC engine torque. Several cases may happen, as follows:

• : Desired torquecan be produced using both the engine and motor;

• : Desired torqueis equal to the maximal torque that can be produced

by the powertrain using the gear ;• : Pure electric

mode—the IC engine speed is not high enough to closethe clutch or the torque demand is equal to the min-imal torque that can be produced using gear ;

• : Torque demandis greater than the powertrain torque capability.

In the same way, the constraints on speed (3), (4) can bewritten as

(12)

is the set of admissible gear numbers such that

1) speed constraints (3), (4) are verified for both the engineand the motor;

2) required torque at the wheel can be produced bythe powertrain, i.e., .

At last, a formulation of the electric power and fuel consump-tion with only the decision variables is obtained from (1), (2)

(13)

(14)

Considering that the IC engine produces the torqueusing the th gear, represents the powerrequired by the motor to ensure the driver desired torque atwheel for the wheel speed . In the same way,

represents the instantaneous IC engine fuel con-sumption required to produce the torque with the thgear. For example, for the parallel single-shaft arrangement[Fig. 1(b)]

• IC engine torque limits andare derived from (6) using (7) and (8) as

(15)

DELPRAT et al.: CONTROL OF A PARALLEL HYBRID POWERTRAIN 875

(16)

• Electric power consumption is obtainedfrom using (7) and (8)

(17)

• Fuel consumption is obtained fromusing (7)

(18)

III. GLOBAL OPTIMIZATION

A. Problem Formulation

The objective is to choose, at each sampling time, the optimalpair of decision variables according to the mini-mization of the total fuel consumption over the speed cycle

(19)

Under mechanical constraints

(20)

This problem has an obvious solution corresponding to, which is called pure electric mode. This

mode will, of course, lead to the battery discharge. To avoid thiscase, a constraint on the battery state of charge is introducedinto the problem (19). For sake of convenience, the followingconstraint is considered:

Soc (21)

With Soc, the desired electric energy consumption overthe speed cycle is called overall state of charge variation. If

Soc , we can consider that, globally speaking, the totalamount of energy for propelling the vehicle has been taken fromthe irreversible source of energy (fuel). In this case, the fuel-con-sumption results can be compared with those of conventionalvehicles.

Thus, the global optimization problem is Criterion (19), underthe mechanical constraints (20) and the state-of-charge con-straint (21).

B. Optimal Control

To apply the classical optimal control theory, the mechanicalconstraint (11) is written as an equality constraint by introducinga parameter

(22)

with and.

A new formulation of problem (19) is obtained by introducingthe dynamic system (13) and the constraint (22) into the crite-rion with and Lagrangian parameters as

(23)

Optimality conditions are given by first- and second-orderderivatives

(24)

(25)

(26)

(27)

(28)

(29)

(30)

(31)

According to (28), two cases may be considered, as follows:

• First case:

then

• Second case: .Criterion (23) becomes

(32)

and constraint (27)

(33)

A way to solve (33) is to expressand as analytical expressions. Letus recall that the fuel consumption andthe motor power consumption are givenby maps. For example, Fig. 3 represents the IC enginefuel consumption over speed and torque.

876 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 3, MAY 2004

Fig. 3. Fuel consumption over speed and torque.

represents the intersections between the planesand the fuel-consumption

map .The resulting curves are then approximated. A very convenient

way is to choose as an approximation of and, a second-order piecewise model. It will provide

a simple first-order piecewise linear model for the derivatives

(34)

(35)

with and the number of models. The ap-proximation accuracy depends only on the number of models

, which is only limited by the number of data contained in themaps. Using (7) and (8) or (9) and (10) allows rewriting (35)with the decision variables

(36)

If is known, the set of solutions with respect to (31)can be obtained replacing (34) and (36) into (33). may beempty or may contain several values. A way to choose the bestvalue is to rewrite (32) as

(37)

At each sample time , the control value is obtained as

(38)

The whole problem (19)–(21) is reduced to the choice of aunique value . For a given speed cycle at each sampling time, the choice of the control depends only on the

value of and, therefore, the final state of charge alsodepends on . The value of that ensures

, with and small enough, is obtained using adichotic search that usually converges in less than ten iterations.This point will be discussed further in the results’ part. In thefollowing, this algorithm is referenced as Algorithm 1.

IV. INTEGRATING A MORE ACCURATE BATTERY MODEL

The electric power consumption map hasbeen computed considering a nominal battery state of charge(80% in our case) and so a mean efficiency. For short speedcycles, this hypothesis seems to be reasonable. Nevertheless,for long trips, nothing guarantees that the state of charge willnot reach values far from its nominal value [10].

To improve the algorithm, a more accurate battery model,based on the charge acceptance [11], is considered for the con-trol law synthesis. This algorithm is referenced as Algorithm 2and (1) is replaced by

(39)

ifif

(40)

represents the power required by themotor to produce the torque at the speed and is

DELPRAT et al.: CONTROL OF A PARALLEL HYBRID POWERTRAIN 877

given as a map over motor torque and speed.is the battery charge acceptance, i.e., the battery efficiency,and depends on the battery current sign and, therefore, on theelectric motor torque sign. Of course, the power considered forAlgorithm 1 corresponds to

A. Problem Formulation

To obtain a formulation of the optimization problem with onlythe decision variables and , (39) and (40) are writtenas with

(41)

ifif

(42)

with andsuch as if .

According to (8) or (10), .At last, we can formulate the optimization problem

System:

(43)

Criterion:

(44)

Constraints:

(45)

Soc (46)

B. Optimal Control

For the sake of convenience, Case 1 corresponds toand Case 2 to .

• Case 1.With , problems (43)–(46) are

similar to (19)–(21). Let us note , the set of so-lutions obtained with conditions (24)–(31).

• Case 2.A new formulation of problem (43) is obtained by intro-

ducing the dynamic system (41) and the torque constraintinto the criterion (44)

(47)

with and Lagrangian parameters. Optimalityconditions are given by first- and second-order derivatives

(48)

(49)

(50)

(51)

(52)

(53)

If , bounds must be considered. Let us note thecorresponding set of solutions

(54)

If after straightforward manipulations, (26) becomeswith

(55)

Thus, . A nonrestrictive hypothesis is toconsider that the state of charge dynamic is very slow accordingto the sampling period used (56). This allows us to simplify thesolution’s search, because the value of can be obtained atthe sample time

(56)

Thus, with

Under the same hypothesis

(57)

(58)

As for Algorithm 1, the electric motor power consumptioncan be approximated using piecewise second-order models

(59)

(60)

Let us recall (34)

Remark: time is omitted when there is no ambiguity.

878 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 3, MAY 2004

Fig. 4. “Routier no. 1” speed cycle.

Introducing (34) and (60) in expression (58) leads to

(61)

(62)

with

At last, a third-order polynomial expression is obtained and(62) is equivalent to

(63)

with

Using the classical Cardan’s method , the set ofsolutions to (63) with respect to and (48)is obtained. Thus, at each sampling time , the control value ischosen in

(64)

At last, the whole problem has been reduced to the choice of aunique parameter . The value of that ensures

, with and small enough, is obtainedusing a dichotic search that usually converges in a few iterations.

Fig. 5. Prototype built at the LAMIH.

V. RESULTS

The vehicle speed set point can be provided by a speed cycle.For example, Fig. 4 represents the “Routier no. 1” speed cycle,which will be used for the presented simulations. It correspondsto real speed data.

A. Prototype Build at the LAMIH

To be close to a real configuration, we have chosen the testedand validated model of a prototype of parallel hybrid vehiclebuilt at the LAMIH [2] (Fig. 5). Of course, as previously stated,the proposed algorithms are flexible enough to deal with dif-ferent arrangements and/or components. The vehicle is a par-allel single-shaft prototype with a 43-kW direct current (dc)motor powered by a 240-V 26 hA pure lead acid battery. TheIC engine is a 1.4l petrol engine with an automated clutch. Thegearbox has been especially designed to handle the maximaltorque of the engine and the motor simultaneously. It has twogears that are close to the second and fifth gears of a conven-tional car. A reductor ensures the mechanical coupling betweenthe engine and the motor and its ratio is such that both the en-gine and motor reach their maximal speeds simultaneously.

In every case (Algorithm 1 and Algorithm 2), the results aregiven by applying the controls to the complete model calledmodel 1.

DELPRAT et al.: CONTROL OF A PARALLEL HYBRID POWERTRAIN 879

Fig. 6. x(N) � x(0) over �(0).

Fig. 7. Results for the Routier no. 1 speed cycle.

B. Algorithm 1

Fig. 6 represents, on the Routier no. 1 speed cycle,. The different tests (speed cycles, mechanical ar-

rangements, components, etc.) made with these algorithms haveshown the same kind of “smooth” and quasimonotonic behaviorof ; thus, a dichotic search is quite efficient. Ofcourse, if it is not the case, functions with several minimumsand maximums and another research algorithm for mustbe implemented.

For example, for Soc , the dichotic search convergesin nine iterations to the value , ensuring aglobal state of charge variation of %, in less than 2 min.The results for this case are presented in Fig. 7 and give a fuelconsumption of 6.9 l/100 km.

A crucial point when designing a real-time control strategyis to choose between the optimization of the instantaneousfuel-consumption minimization and the instantaneous effi-ciency maximization. Clearly, the first choice will lead to lowIC engine torque values and the second to higher torque values.There is no intuitive way to choose between both. The proposedalgorithm may provide an answer to this question.

For the Routier no. 1 speed cycle, Fig. 8 shows the IC engineoperating points in the ( , ) plane. The so-called “optimaltorque” correspondes to torques, maximizing the IC engine ef-ficiency. Isoefficiency curves have also been represented. Wecan notice that IC engine operating points are “often” chosenin high efficiency area. However, due to the constraints that re-duce the choice of the IC engine torque, some points remain inthe low-efficiency area. For example, during braking phases, themotor torque constraint (6) leads to low IC engine torque valuesand, therefore, to a low IC engine efficiency.

The IC engine operating points are often chosen as to be asclose as possible to the “optimal” torque curve. This trend isconfirmed by many experiments on different speed cycles anddifferent overall state of charge variations. For a more completeanalysis that allows deriving a real time control strategy, thereader may refer to [14].

VI. DISCUSSION AND CONCLUSION

To compare the performances of the two algorithms, in bothcases, the fuel consumption is plotted as a function of the overallstate charge variation (Fig. 9).

880 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 3, MAY 2004

Fig. 8. Analysis of the IC engine efficiency.

Fig. 9. Comparison of results obtained using both algorithms.

Results of Algorithm 2 (Fig. 9) are slightly better (about 3%),but more time consuming (between 5 to 10 times slower thanAlgorithm 1). They confirm what was expected. For short speedcycles, the state of charge variation is not large enough to createsignificant differences between the algorithms. That means that

Algorithm 1 is validated for simulation studies. For long speedcycles, it may appear that cases in which significantdifferences intheresultsoccur, indicatingapreferencein theuseofAlgorithm2.

At last, let us recall that both algorithms give an optimal so-lution on the considered model and then give a lower bound of

DELPRAT et al.: CONTROL OF A PARALLEL HYBRID POWERTRAIN 881

fuel consumption in a short time. They are, of course, subop-timal on model 1. However, they can be viewed as an “ideal”case, i.e., the solution may be unrealistic for real driving. Thus,their principal interest is to be the reference for the evaluationof fuel-consumption results obtained with other methods. Everyother global method, i.e., in the sense of giving a global optimalsolution, may claim the same interest. The following methodshave been already tested.

• Simulated annealing has been applied to this optimizationproblem [7]. Two main drawbacks can be noticed. Thefirst is the difficulty to tune its parameters and to makethem evolve with a change of model. The second is not toguarantee a global optimal solution, even for model 2, ina reasonable time.

• Dynamic programming has been applied to energy-man-agement optimization for hybrid vehicles [8], [9]. The realproblem of this method is that it requires a lot of com-putation to provide a solution. Keeping the same modelsas those proposed in this paper, a unique overall state-of-charge variation Soc computation takes about 1 day.

Finally, the proposed algorithm is also helpful for the following.• Design of Powertrains: During its design, it is difficult to

evaluate the future powertrain efficiency. Either it can becomputed using components mean efficiency that are notrealistic under real driving conditions or it can be evaluatedusing powertrain simulations over speed cycles. However,in this case, the results are dependant on the chosen controlstrategy. The proposed algorithm avoids this drawback,providing the powertrain potential maximal efficiencywithout having to design a control strategy. Moreover, it isalso possible to select the components of the powertrain ac-cording to their influence on the global energetic efficiency.

• Evaluation of Real-Time Control Strategies: Evaluatinghybrid vehicle fuel consumption cannot be reduced to thecomparison of fuel consumption over a speed cycle witha null overall state of charge variation. For a given speedcycle, the fuel consumption can be expressed as a functionof the overall state of charge variation and the results of thealgorithm provides the minimum fuel-consumption curve.Every real-time control strategy will generate a fuel-con-sumption curve that can be compared to the minimumcurve [13].

REFERENCES

[1] F. L. Lewis and V. L. Syrmos, Optimal Control. New York: Wiley,1995.

[2] G. Paganelli, J. J. Santin, T. M. Guerra, A. Noel, M. Delhom, E.Combes, and J. E. Guy, “Conception and control of parallel hybrid carpowertrain,” in Proc. Electric Vehicle Symp. 16, Bruxelles, Belgium,Oct. 1998, pp. 215–216.

[3] J. S. Won and R. Langari, “Fuzzy torque control for a parallel hybridvehicle,” in Proc. Int. Mech. Eng. Conf. Expo., 2001.

[4] M. Salman, N. J. Schouten, and N. A. Kheir, “Control strategies for par-allel hybrid vehicle,” in Proc. Amer. Control Conf., Chicago, IL, June2000.

[5] J. Seiler and D. Schröder, “Hybrid vehicle operating strategies,” in Proc.Elect. Veh. Symp. 15, Bruxelles, Belgium, Oct. 1998.

[6] G. Paganelli, T. M. Guerra, S. Delprat, J. J. Santin, M. Delhom, andE. Combes, “Simulation and assesment of power contol strategies for aparallel hybrid car,” J. Autom. Eng., no. 214, pp. 705–718, 2000.

[7] S. Delprat, G. Paganelli, T. M. Guerra, J. J. Santin, M. Delhom, and E.Combes, “Algorithmic optimization tool for the evaluation of HEV con-trol strategies,” in Proc. Electric Vehicle Symp. 16, Beijing, China, 1999.

[8] A. Brahma, Y. Guezennec, and G. Rizzoni, “Optimal energy manage-ment in series hybrid vehicles,” in Proc. Amer. Control Conf., Chicago,IL, June 2000.

[9] S. Rimaux, M. Delhom, and E. Combes, “Hybrid vehicle powertrain:modeling and control,” in Proc. Elect. Veh. Symp. 16, Beijing, China,Oct. 1999.

[10] S. Delprat, T. M. Guerra, G. Paganelli, J. Lauber, and M. Delhom, “Con-trol strategy optimization for an hybrid parallel powertrain,” in Proc.Amer. Control Conf., Arlington, VA, June 2001, pp. 1315–1320.

[11] J. A. Magyar, M. A. Kepros, and R. F. Nelson, “Reference electrodeand gasing studies of lead/acid charge/discharge processes,” J. PowerSources, vol. 31, pp. 93–106.

[12] G. Paganelli, “Conception et commande d’une chaîne de traction opti-misée pour véhicule hybride parallèle thermique et électrique,” Ph.D.dissertation, Laboratoire d’Automatique et de Mécanique Industrielleset Humaines, Univ. Valenciennes, Valenciennes, France, 1999.

[13] S. Delprat, T. M. Guerra, and J. Rimaux, “Optimal control of a parallelpowertrain: From global optimization to real time control strategy,” inProc. Elect. Veh. Symp. 18, Berlin, Germany, 2001.

[14] , “Evaluation de stratégies de commande pour véhicules hybridesparallèles,” in Proc. Conf. Int. Francophone d’Automatique, Nantes,France, 2002.

Sebastien Delprat was born in Muret, France, in1976. He received the Ph.D. degree in automaticcontrol from the University of Valenciennes et duHainaut-Cambrésis (UVHC), France, in 2001.

He is an Assistant Professor at UVHC. His mainresearch interests are hybrid vehicle control, vehicledynamics, and fuzzy control.

Dr. Delprat is a Member of the Fuzzy SystemsResearch Group, Laboratoire d’Automatique,de Mécanique et d’Informatique Industrielles etHumaines and of the IEEE Vehicle Power and

Propulsion Committee.

Jimmy Lauber was born in Tours, France, in1976. He received the Ph.D. degree in automaticcontrol from the University of Valenciennes et duHainaut-Cambrésis (UVHC), France, in 2003, wherehe studied modeling and control of IC engines withEGR.

He is a Temporary Assistant Professor at theUVHC. His research interests include nonlinearand fuzzy controls and their applications to the ICengine.

Thierry Marie Guerra was born in Mulhouse,France, in 1963. He received the Ph.D. degree in au-tomatic control from the University of Valencienneset du Hainaut-Cambrésis (UVHC), France, in 1991and the HDR degree in 1999

He is a Professor at the UVHC and heads theFuzzy Systems Research Group, Laboratoired’Automatique, de Mécanique et d’InformatiqueIndustrielles et Humaines (LAMIH UMR CNRS8530). He is also Vice President of the GRAISyHM,a research group in integrated automation and

man–machine systems that includes 220 researchers from ten laboratories ofthe Région Nord Pas de Calais, France. His major research fields are nonlinearcontrol, fuzzy control, and optimal control and their applications to powertrainsystems (IC engines, electrical motors, hybrid vehicles, etc.).

Dr. Guerra is a Member of the IEEE Vehicle Power and Propulsion Committeeand the IFAC TC3.2 Cognition and Control.

J. Rimaux was an Assistant Professor in the Con-trol Systems Department, University Simon Bolivar,Caracas, Venezuela, from 1993 to 1998. Since 1999,she has been with in the Division of Research, PSAPeugeot Citroën, where she is involved with the hy-brid vehicle project.