Adaptive H∞ Control Using Backstepping Design and Neural Networks

In this paper, the adaptive H∞ control problem based on the neural network technique is studied for a class of strict-feedback nonlinear systems with mismatching nonlinear uncertainties that may not be linearly parametrized. By combining the backstepping technique with H∞ control design, an adaptive neural controller is synthesized to attenuate the effect of approximation errors and guarantee an H∞ tracking performance for the closed-loop system. In this work, the structural property of the system is utilized to synthesize the controller such that the singularity problem of the controller usually encountered in feedback linearization design is avoided. A numerical simulation illustrating the H∞ control performance of the closed-loop system is provided.

[1]  M. Polycarpou,et al.  Stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators , 1998 .

[2]  Tsai-Yuan Lin,et al.  An H∞ design approach for neural net-based control schemes , 2001, IEEE Trans. Autom. Control..

[3]  I. Kanellakopoulos,et al.  Adaptive nonlinear control without overparametrization , 1992 .

[4]  P. Kokotovic,et al.  Adaptive nonlinear design with controller-identifier separation and swapping , 1995, IEEE Trans. Autom. Control..

[5]  I. Kanellakopoulos,et al.  Systematic Design of Adaptive Controllers for Feedback Linearizable Systems , 1991, 1991 American Control Conference.

[6]  Ken-ichi Funahashi,et al.  On the approximate realization of continuous mappings by neural networks , 1989, Neural Networks.

[7]  Masayoshi Tomizuka,et al.  Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form , 1997, Autom..

[8]  Bor-Sen Chen,et al.  H∞ tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach , 1996, IEEE Trans. Fuzzy Syst..

[9]  Marios M. Polycarpou,et al.  A Robust Adaptive Nonlinear Control Design , 1993, 1993 American Control Conference.

[10]  Li-Chen Fu,et al.  Neural network approach to variable structure based adaptive tracking of SISO systems , 1996, Proceedings. 1996 IEEE International Workshop on Variable Structure Systems. - VSS'96 -.

[11]  Rong-Jong Wai,et al.  Intelligent backstepping control for linear induction motor drive , 2001 .

[12]  Marios M. Polycarpou,et al.  Stable adaptive neural control scheme for nonlinear systems , 1996, IEEE Trans. Autom. Control..

[13]  Heinz Unbehauen,et al.  ANNNAC-extension of adaptive backstepping algorithm with artificial neural networks , 2000 .

[14]  Tsu-Tian Lee,et al.  Hinfin tracking-based sliding mode control for uncertain nonlinear systems via an adaptive fuzzy-neural approach , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[15]  A. Annaswamy,et al.  Adaptive control of nonlinear systems with a triangular structure , 1994, IEEE Trans. Autom. Control..

[16]  Frank L. Lewis,et al.  Robust backstepping control of induction motors using neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

[17]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[18]  Jooyoung Park,et al.  Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.

[19]  Frank L. Lewis,et al.  Robust neural network control of flexible-joint robots , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[20]  C.-L. Lin,et al.  Approach to adaptive neural net-based H∞ control design , 2002 .

[21]  Visakan Kadirkamanathan,et al.  Dynamic structure neural networks for stable adaptive control of nonlinear systems , 1996, IEEE Trans. Neural Networks.

[22]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[23]  Robert M. Sanner,et al.  Gaussian Networks for Direct Adaptive Control , 1991, 1991 American Control Conference.

[24]  Bor-Sen Chen,et al.  Robustness design of nonlinear dynamic systems via fuzzy linear control , 1999, IEEE Trans. Fuzzy Syst..

[25]  Tsu-Tian Lee,et al.  Adaptive fuzzy control for strict-feedback canonical nonlinear systems with H infin tracking performance , 2000, IEEE Trans. Syst. Man Cybern. Part B.

[26]  Y. Shrivastava,et al.  Adaptive H∞ neural network tracking controller for electrically driven manipulators , 1998 .

[27]  Frank L. Lewis,et al.  Feedback linearization using neural networks , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).