Direct and Indirect Robust Adaptive Fuzzy Controllers for a Class of Nonlinear Systems

Transcription

1 46 International Jornal Najib Essonboli of Control, Atomation, and Abdelaziz and Hamzaoi ystems, vol 4, no, pp 46-54, April 6 Direct and Indirect Robst Adaptive Fzzy Controllers for a Class of Nonlinear ystems Najib Essonboli and Abdelaziz Hamzaoi Abstract: In this paper, we propose direct and indirect adaptive fzzy sliding mode control approaches for a class of nonaffine nonlinear systems In the direct case, we se the implicit fnction theory to prove the existence of an ideal implicit feedback linearization controller, and hence approximate it to attain the desired performances In the indirect case, we exploit the linear strctre of a akagi-geno fzzy system with constant conclsion to establish an affine-in-control model, and therefore design an indirect adaptive fzzy controller In both cases, the adaptation laws of the adjstable parameters are dedced from the stability analysis, in the sense of Lyapnov, to get a more accrate approximation level In addition to their robstness, the design of the proposed approaches does not reqire the pper bonds of both external distrbances and approximation errors o show the efficiency of the proposed controllers, a simlation example is presented Keywords: Adaptive fzzy control, nonaffine systems, nonlinear systems, sliding mode control INRODUCION Adaptive control schemes for nonlinear systems via feedback linearization concept have been widely employed for decades he idea of feedback linearization approaches is to transform a nonlinear dynamic system into a linear system throgh state feedback mechanisms With sch transformations, those well-explored linear controllers can then be applied to meet desired control specifications everal reslts and parameter adaptive control schemes have been reported in [-3] However, the performances of these approaches are directly relied to the exact cancellation of nonlinear terms If these nonlinear terms are ncertain or nknown, the performances can be deteriorated de to non-exact cancellation As a model free design method, fzzy systems have been sccessflly applied to control complex or illdefined processes whose mathematical models are difficlt to obtain [4-5] he ability of converting lingistic descriptions into atomatic control strategy makes it a practical and promising alternative to the classical control scheme for achieving control of complex nonlinear systems A major drawback of fzzy control systems is that the fzzy rles mst be previosly tned by trial and error procedres o Manscript received October, 5; accepted Janary, 6 Recommended by Editor Zengqi n Najib Essonboli and Abdelaziz Hamzaoi are with the Mechanical Engineering Department of the echnical Institte of royes, 9, re de Qebec, BP royes cedex- France ( s: {najibessonboli, abdelazizhamzaoi}@ niv-reimsfr overcome this problem, some research has been focsed on the Lyapnov synthesis approach to constrct stable adaptive fzzy controllers [6-] he basic idea of most of these works is that with the niversal approximation ability of fzzy systems [], the plant model is approximated by two adaptive fzzy systems to constrct the control law o make more accrate the approximation level and hence to improve the tracking performances, the adaptation laws of the adjstable parameters are synthesised from the stability analysis in the sense of Lyapnov o maintain the performance of fzzy adaptive control in the presence of external distrbances, some robst schemes based on sliding mode control or H techniqe are presented in the literatre [-4] However, these approaches are restricted to affine in control plants o overcome this restriction, some works treating the extension of adaptive control to nonaffine systems have been developed in the literatre Concerning the indirect adaptive control scheme, there are two techniqes where the main idea is to synthesise an affine-in-control model of the plant to design the controller Indeed in [5] and [6], the athors exploit the linear strctre of the akagi- geno systems with trianglar membership fnctions for inpts and constant conclsion, to establish an affine-in-control fzzy model to describe the dynamic behavior of the plant In [7], the aylor series expansion is sed to obtain an affine in a control model of the plant Concerning the direct control scheme presented in [8,9], the athors sed the implicit theorem and variable strctre control to prove the existence of feedback control, which has

2 Direct and Indirect Robst Adaptive Fzzy Controllers for a Class of Nonlinear ystems 47 been approximated sing neral networks o improve the approximation level and hence the tracking performances, an adaptation law is derived from the stability analysis However, to ensre the stability and the robstness of the closed loop system in these works, an additional control signal is needed to compensate the approximation errors and the external distrbances he design of this signal depends on the well-known pper bonds of both the approximation errors and the external distrbances, which is a restrictive assmption de to the fact that these bonds are generally nknown In this work, we propose direct and indirect adaptive fzzy controllers for a class of non-affine systems sbject to external distrbances In the direct case, we se an adaptive fzzy system to approximate the implicit desired feedback control whose existence is proven by the implicit theorem In the indirect case, we exploit the linear strctre of a akagi-geno fzzy system to generate a fzzy affine-in-control model to approximate the dynamic behavior of the plant In both cases, we tilize the modified sliding mode control to ensre the robstness of the closed loop system Indeed, the approaching phase is assred by an attenation term that allows the chattering phenomenon to be eliminated and the constraint on the knowledge of the pper bonds of both external distrbances and approximation errors to be overcome o improve the approximation level, the adaptation laws are derived from the stability analysis in the sense of Lyapnov o show the efficiency of the proposed approaches, an illstration example is presented PROBLEM AEMEN Consider a single-inpt single-otpt (IO nonlinear system described by the following differential eqation: ( ( n,,, ( n y = f y y y, + d, ( where y R is the measred otpt, R the control inpt, ( i y, i =,, n, is the i th time derivative of y, f ( is an nknown nonlinear continos fnction, and d is the external distrbances assmed to be nknown bt bonded Withot loss of generality, we assme that all the state variables ( [,, ],, n x= x xn = y y are available to the measrement he objective is to develop a control law sing sliding mode control to ensre the tracking performances and the robstness of the closed loop system o, forcing the system to track a reference trajectory is eqivalent to forcing the plant to attain a sliding srface and to maintain it on it he Hrwitzian strctre of this srface allows the convergence of the plant to the phase plan origin 3 DIREC ADAPIVE FUZZY CONROLLER In this section or task is to synthesise a direct adaptive fzzy controller for the system ( For this, we assme the following: f ( x, Assmption A: b = > b Assmption A: here exists a smooth fnction b b / t b x b b β ( x > sch that = β ( o attain the desired tracking performances, let s consider the sliding srface or the filtered error given as follows [3]: ( n ( n =e k e k e ( n ( i =e k ie, n n ( where e= yr y denotes the tracking error and y r is a bonded reference trajectory he gains k i, i =,, n, are chosen sch that the corresponding polynomial is Hrwitzian Using ( and (, the time derivative of the switching srface can be written as: ( n ( i =e k e ( n, ( i = f x + d y ke ( n i r n i (3 Lemma [9]: For the system ( free of external distrbances (d= satisfying A and A, there exists a compact set Φ and an niqe ideal inpt sch that all x( Φ, the eqation (3 can be expressed as the following form: ( =β x, (4 which allows to obtain lim y y = x he previos lemma garantees only the existence of a control law garanteeing the convergence of the tracking error toward zero and does not provide the method of constrcting it [9] Based on the fact that a fzzy system is an niversal approximator [], we r

3 48 Najib Essonboli and Abdelaziz Hamzaoi se a fzzy akagi-geno system to approximate the ideal law o garantee the stability of the closed loop system, we add a spplementary signal s Hence, the proposed control law is given by: = +, (5 fzzy s fzzy s ( x = θ Ψ, (6 =, (7 where θ is the vector of the adjstable parameters, Ψ ( x the regressive vector, and is a positive constant representing the attenation level of the effects of both the approximation error and the external distrbances Note that is written as = θ Ψ x + δ, where θ is the optimal vale of ( θ and δ is the approximation error Using the Mean Vale heory [3], there exists a λ, sch that: positive constant ] [ (, (, λ ( f x = f x + b, (8 ( x, f where b λ = and λ = λ+ ( λ = λ According to the implicit theorem [3, there exists a v f x, v= β x sch that ( n + = where ( ( n ( i y k e o, (8 can be written as: r i (, = + λ ( n ( n ( i = β ( x + yr + kie + bλ ( f x v b From (3 and (9, we can obtain: ( λ ( (9 = β x + b + d ( Using (5, eqation ( becomes: or ( = β x + b + b λθ λ fzzy λ s ( b Ψ x b δ + d λ ( ( ( = β x + b θ Ψ x b θ Ψ x λ bλ b, λδ + d λ ( ( = β( x + b λθ Ψ( x bλ b λδ + d,(3 which gives b λ = b λβ( x + θ Ψ( x δ + b λd,(4 where θ = θ θ Consider the following Lyapnov fnction: V = bλ + θ θ (5 η Differentiating (5 along ( yields: V = b λ + bλ + θ θ + θ θ (6 η η Using the fact that θ = θ θ = θ and since the elements of V are scalars, the eqation (6 can be rewritten as: V = b λ + θ θ η = bλβ ( x + θ Ψ( x b λδ + bλd + θ θ η = bλβ ( x + θ Ψ( x ( δ bλd + θ θ η =bλβ( x ( δ b ( ( λd + θ θ + ηψ x η ( δ b ( ( λd + θ θ + ηψ x η (7 Choosing the following adaptation law: θ =ηψ x (8 gives: ( ( δ λ V b d ( δ λ b d b d b d + + ( δ λ ( δ λ ( δ bλ d + + ( δ bλ d (9

4 Direct and Indirect Robst Adaptive Fzzy Controllers for a Class of Nonlinear ystems 49 Integrating the above ineqality from t = and, we have: ( ( + ( δ λ,( V V dt b d dt dt V ( V ( + ( δ b λd dt ( Using the fact that V(, the above ineqality can be simplified as: + ( ( δ λ, ( dt V b d dt ( garantees that L Becase all the variables in the right-hand side of (4 are bonded, ie, L ince the right side of ( are also bonded, L [8,9] Using Barbalat Lemma, we have when t [9] herefore, the tracking error converges to the origin, ie, lim e = [3] x o ensre the convergence of the adaptive algorithm, we introdce the projection algorithm defined by (3 : if [ θ max ] ηψ ( x or[ θ = max θ = and Ψ( x ] θθ : if [ θ = max η ( x ( x Ψ + Ψ θ and Ψ ( x < ] (3 4 INDIREC ADAPIVE FUZZY CONROLLER In the case where Assmptions A and A are restrictive, and we cannot satisfy them, we can se an indirect adaptive fzzy controller he main idea is to constrct an affine model of the plant sing a akagi- geno system hen we se it to synthesise a robst controller allowing it to ensre the tracking performances and the robstness of the closed loop system he plant is constrcted from a akagi-geno system whose inpts are the state variables x, i =,, n, and For each variable x, i =,, n, and, we define p i and M fzzy sets Hence, the j th rle can be written in the form: Rle j IF x is A And xnis An And is B ( j,, jn, m HEN x n = θ, where ji {,, pi} j n m for i,, n (4 = and m {,, M} ( j,, jn, m θ is a constant corresponding to the j th rle j where the fzzy sets,, jn, m A An B are sed Using the singleton fzzifier, the centre average defzzification and the prodct inference engine, the otpt of the akagi-geno system can be given by [8]: p pn n M ( j,, jn, m θ μ ji ( xi μ m ( B Ai j jn i = x n = p pn M n, (5 μ ji ( xi μ B m ( Ai j jn i = or on the following vectorial form: xn =Θ Ψ( x, where ( x, vector with its (,,,, (6 Ψ is a p pn M dimensional th j jn m element given by: n μ ji ( xi μ m( ( j,, jnm, Ai B i = Ψ = p pn M n μ ji ( xi μ m( Ai j jn i = B, (7 and (,,, ( p,, pn, M Θ= θ,, θ denotes the vector of the adjstable parameters Let s consider that the membership fnctions of lingistic variables of have the form of a triangle and are placed evenly throghot the whole defined space U as illstrated in Fig he space U can Fig he membership fnctions of

5 5 Najib Essonboli and Abdelaziz Hamzaoi be decomposed into several sbspaces U, =,,, M [5] If exists in the sbspace U, all membership fnction vales are given by: μ where m B ( am+ m = am a m+ am = m= + am am otherwise, a m is a constant satisfying ( B m a m For a given vale of {,,, M } inpt exists in the sbspace (8 in (5 gives: p μ = (8 =, the control U o, sbstitting ˆ ( j,, jn, ( j,, jn, + f ( x,, Θ = Ψ s aθ a+ θ where j jn p pn Ψs j jn + pn ( x ( =Φ +Φ Ψ s = a ( j,, jn, ( j,, jn, + θ θ x, (9 ( xi ( x ( n μ ji A i = i p pn M n a + μ ji i μ B m Ai j jn i = herefore, the fzzy system can be decomposed into M- sbsystems, which allows to obtain an affine-in-control model of the plant [5,6] After synthesising the fzzy model, or next task is to develop a robst controller to ensre the global stability and the robstness of the closed loop system o, the proposed control law is given by: n ( n ( i = Φ ( x Φ ( x + yr + kie + s,(3 where s denotes an additional term garanteeing the robstness of the closed loop system by attenating the effects of both the external distrbances and the approximation errors to a prescribed level o attain this objective, we choose s as given in (7: s = Using (3, the time derivative of the sliding srface is given by: ( ˆ ( = f x, f x,, Θ + s + d (3 ˆ,, Θ =Θ Ψ, the optimal If we note by f ( x ( x vale of f ˆ ( x,, Θ =Θ Ψ ( x, and by w= f ( x, ( x ˆ f,, Θ the minimal approximation error, (3 can be rewritten as: (, = +Θ Ψ +, (3 w x d o determine the adaptation law of the adjstable parameter vector Θ, we consider the following Lyapnov fnction: V = + Θ Θ, (33 σ where σ is a positive constant given by the designer Using (3 and the fact that Θ=Θ, the time derivative of (33 can be written as: V = w+θ Ψ ( x, + d Θ Θ, (34 σ V = [ w+ d] Θ Θσ Ψ( x, σ, (35 V = [ w+ d] Θ Θσ Ψ( x, σ,(36 V = [ w+ d] [ w+ d] (37 + [ w+ d] Θ Θ σψ( x,, σ V = w+ d w d + + Θ Θ σ Ψ( x,, σ [ ] [ ] (38 V [ w+ d] Θ Θσ Ψ( x, σ (39 If we choose the following adaptation law: (, Θ= σ Ψ x (4 and sing the same mathematical tool development presented in the previos section, we can obtain: dt V w d dt ( + [ + ] (4 As proven in the previos section, we have L

6 Direct and Indirect Robst Adaptive Fzzy Controllers for a Class of Nonlinear ystems 5 and L Hence, we have when t According to the Hrwitzian strctre of the sliding srface, the system converges to the origin of the phase plan [3] Remark : o overcome the singlarity problem when ( x Φ = withot complicating the controller strctre, we propose to sbstitte the term Φ ( x Φ ( x by [33] which yields ε + Φ ( x the new control law: Φ ( x n ( n ( i ( r i s,(4 ( i x = = Φ x + y + ke + ε + Φ where ε is a small positive constant Remark : o ensre the convergence of the adaptive algorithm, we modify the adaptation law by sing the projection techniqe as given by (43 : if [ Θ fmax ] σ Ψ( x, or[ Θ = fmax Θ= and Ψ( x, ] : if [ Θ = f ΘΘ max σ ( x, ( x Ψ Ψ and Ψ > Θ ( x 5 AN ILLURAION EXAMPLE, ] (43 o illstrate the effectiveness of the proposed adaptive controllers, we consider the following system: x = x 3 x = x + + ( + x + sin ( (44 y = x In this simlation example, the control objective is to determine so that the otpt y follows the desired reference trajectory yr = sin( t o show the robstness of the proposed approaches, we consider that the system is sbject to external distrbances in the form d = ( sin( t + sin( t o synthesise the direct adaptive fzzy controller, we se a fzzy system with the state variables x₁ and x₂ as inpts and fzzy as otpt For each inpt variable, we define five fzzy sets covering niformly their niverses of discorse [-5,5], whose corresponding membership fnctions are trianglar he plant mst attain the following srface = e + e, and slide on it to reach the origin e = e= Figs, 3 and 4 present the simlation reslts for the initial sate [ x x ] = [ 5 5] and the attenation level = 5 Figs and 3 demonstrate the good tracking performances and the convergence of the state variables to their reference trajectories In ime (s Fig Evoltion of the state variable x (solid line and its reference trajectory (dashed line ime (s Fig 3 Evoltion of the state variable x (solid line and its reference trajectory (dashed line ime (s Fig 4 Applied control signal

7 5 Najib Essonboli and Abdelaziz Hamzaoi Fig 4, we remark that the control signal does not contain any abrpt variation despite the knowledge navailability of the pper bond of the external distrbances o overcome the restrictive assmptions A and A sed to design the control law (5, we propose to se the indirect adaptive fzzy controller given by (3 For this, we mst at first define a fzzy system, which inpts the state variables ( x x and the control inpt, to approximate the dynamic fnction f ( x, he niverse of discorse of the inpts x, x, and are respectively [ ], [ ] and [ 5 5] For each inpt variable, we have defined respectively 5, 5, and 6 lingistic sets Figs 5 and 6 give the evoltion of the state variables x and x together with the corresponding reference signals Despite sing an affine-in-control fzzy model to synthesise the control law, we can note the good tracking performances and the convergence of the system to the desired trajectories his can be jstified ime (s Fig 7 Evoltion of the dynamic fnction f ( x, (dashed line and its approximation (continos line ime(s Fig 5 Evoltion of the state variable x (solid line and its reference trajectory (dashed line ime(s Fig 6 Evoltion of the state variable x (solid line and its reference trajectory (dashed line ime(s Fig 8 Applied control signal by the good approximation level assred by the proposed approach as illstrated in Fig 7 he applied control signal to attain or objective is given by Fig 8 In smmary, we can conclde that the proposed approaches (direct and indirect schemes allow the desired tracking performances to be attained and also ensre the robstness of the closed loop system, withot sing classical methods of linearization Frthermore, the design of these controllers does not reqire any knowledge regarding the distrbances strctre or their bonds 6 CONCLUION In this paper direct and indirect robst adaptive fzzy controllers for a class of nonaffine nonlinear systems are presented In the direct case, based on the implicit theorem, a fzzy adaptive system is sed to attain the desired performances In the indirect case, a akagi-geno system is sed to synthesise an affinein-control model, and hence to design the controller In the two cases, the robstness of the closed loop system is garanteed by a modified sliding mode

8 Direct and Indirect Robst Adaptive Fzzy Controllers for a Class of Nonlinear ystems 53 control where the pper bonds of both the external distrbances and the approximation errors are not reqired o improve the approximation accracy, the adaptation laws of the adjstable parameters are dedced from the stability analysis in the sense of Lyapnov he simlation reslts demonstrate both good tracking performances and high efficiency of theses approaches Crrent works are focssed on the se of a state observer to overcome the assmption on the availability of the state variables to the measrement REFERENCE [] A Isodori, Nonlinear Control ystems, pringerverlag, 989 [] astry and M Bodson, Adaptive Control: tability, Convergence, and Robstness, Prentice- Hall, Englewood Cliffs, NJ, 989 [3] J J E lotine and W Li, Applied Nonlinear Control, Prentice-Hall, 99 [4] P J King and E P Mamadani, he application of fzzy control systems to indstrial process, Atomatica, vol 3, pp 35-4, 977 [5] akagi and M geno, Identification of systems and its applications to modeling and control, IEEE rans on ystems, Man and Cybernetics, vol 5, pp 6-3, 985 [6] J pooner and K M Passino, table adaptive control of a class of nonlinear systems and neral network, IEEE rans on Fzzy ystems, vol 4, pp , 994 [7] C Y e and Y tepanenko, Adaptive control of a class of nonlinear systems with fzzy logic, IEEE rans on Fzzy ystems, vol, pp 85-94, 994 [8] L-X Wang, Adaptive Fzzy ystems and Control, Prentice-Hall, Englewood Cliffs, New Jersey, 994 [9] L-X Wang, table adaptive fzzy controllers with application to inverted pendlm tracking, IEEE rans on ystems, Man and Cybernetics, vol 6, pp , 999 [] C ong and Y Chai, Fzzy adaptive control for a class of nonlinear systems, Fzzy ets and ystems, vol, pp 3-39, 999 [] L-X Wang Fzzy systems are niversal approximators, Proc of International Conference on Fzzy systems, an Diego, CA, UA, pp 63-7, 99 [] A higame, Frkawa, Kawamoto, and anigchi, liding mode controller design based on fzzy inference for nonlinear systems, IEEE rans on Indstrial Electronics, vol 4, pp 64-7, 993 [3] L-X Wang, A Corse in Fzzy ystems And Control, Prentice-Hall PR, Upper addle River, New Jersey, 997 [4] A Hamzaoi, N Essonboli, and J Zaytoon, Fzzy sliding mode control with fzzy switching fnction for nonlinear ncertain MIMO systems, Jornal of ystems and Control Engineering, vol 8, pp 87-97, 4 [5] B Yoo and W Ham, Adaptive fzzy sliding mode control of nonlinear systems, IEEE rans on Fzzy ystems, vol 6, pp 35-3, 998 [6] J Wang, A B Rad, and P Chan, Indirect sliding mode control: part I: Fzzy switching, Fzzy ets and ystems, vol, pp -3, [7] W- Lin and C- Chen, Robst adaptive sliding mode control sing fzzy modeling for a class of ncertain MIMO nonlinear systems, IEE Proc of Control heory Application, vol 49, pp 93-, [8] A Hamzaoi, N Essonboli, and J Zaytoon, Fzzy sliding mode control for ncertain IO systems, Proc of IFAC International Conference on Intelligent Control ystems and ignal Processing, Faro, Portgal, vol, pp 33-38, April 3 [9] B- Chen, C-H Lee, and Y-C Chang, H tracking design of ncertain nonlinear IO systems: Adaptive fzzy approach, IEEE rans on Fzzy ystems, vol 4, pp 3-4, 996 [] A Hamzaoi, J Zaytoon, and A Elkari, Adaptive fzzy control for ncertain nonlinear systems, Proc of IFAC Workshop on Control Applications of Optimization, aint-petersbrg, Rssia, pp 49-5, [] A Hamzaoi, A Elkari, and J Zaytoon, Robst adaptive fzzy control application to ncertain nonlinear systems in robotics, Jornal of ystems and Control Engineering, vol 6, part, pp 5-35, [] Y-C Chang, Adaptive fzzy-based tracking control for nonlinear IO systems via V and H approaches, IEEE rans on Fzzy ystems, vol 9, no, pp 78-9, [3] N Essonboli, A Hamzaoi, and J Zaytoon, A spervisory robst adaptive fzzy controller, Proc of 5th IFAC World Congress on Atomatic and Control, Barcelona, pain, [4] N Essonboli, A Hamzaoi, K Benmahammed, and J Zaytoon, A robst adaptive fzzy control applied to distrbed MIMO systems, Proc of IEEE Conference on Control Applications, Glasgow, cotland, pp 38-43, [5] P- Yoon, J-H Park, and G- Park, Adaptive fzzy control of nonlinear systems sing akagi- geno fzzy models, Proc of IEEE International Fzzy ystems Conference, pp ,

9 54 Najib Essonboli and Abdelaziz Hamzaoi [6] R Bokezzola, Galichet, and L Folloy, Fzzy adaptive linearizing control for nonaffine systems, Proc of IEEE International Fzzy ystems Conference, pp , 3 [7] J H Park and G Park, Robst adaptive fzzy controller for non-affine nonlinear systems with dynamic rle activation, International Jornal of Robst and Nonlinear Control, vol 3, pp 7-39, 3 [8] X Go, Y Han, Y H, and Y Zhang, CMAC NN-based adaptive control of non-affine nonlinear systems, Proc of 3rd World Congress on Intelligent Control and Atomation, Hefei, China, pp , [9] Zhang, Ge, and C C Hang, Direct adaptive control of non-affine nonlinear systems sing mltilayer neral network, Proc of the American Control Conference, Philadelphia, pp 55-59, 998 [3] H K Khalil, Nonlinear ystems, Prentice-Hall, 996 [3] C J Gho, Model reference control of nonlinear systems via implicit fnction emlation, International Jornal of Control, vol 6, no, pp 9-5, 994 [3] Ge, H Lee, and J Wang, Adaptive control of non-affine nonlinear systems sing neral networks, Proc of the 5th IEEE International ymposim on Intelligent Control, Rio, Greece, pp 3-8, [33] Labiod, M Bocherit, and M Gerra, Adaptive fzzy control of a class of MIMO nonlinear systems, Fzzy ets and ystems, vol 5, no, pp 59-77, 5 Najib Essonboli received his Maitrise from the University of ciences and echnology of Marrakech (FG in Morocco, his DEA in, and his PhD in 4 from Reims University of Champagne- Ardenne, all in Electrical Engineering ince eptember 5, he has been an Assistant Professor with IU of royes, Reims University His crrent research interests are in the areas of fzzy logic control and robst adaptive control Abdelaziz Hamzaoi received his degree in Electrical Engineering from the Polytechnic chool of Algiers (ENPA, Algeria, in 98; and his DEA (989 and PhD (99 from Reims University of Champagne- Ardenne, both in Electrical Engineering He is a crrently a Professor and Head of the Mechanical Engineering Department of IU at royes, Reims University His research interests inclde intelligent control, fzzy control, and robst adaptive control