Adaptive dynamic surface control for a class of uncertain nonlinear systems in pure-feedback form

In this paper, by incorporating the dynamic surface control technique into a neural network based adaptive control design framework, we have developed a backstepping based control design for a class of nonlinear systems in purefeedback form with arbitrary uncertainty. Our development is able to eliminate the problem of “explosion of complexity” inherent in the existing method. In addition, the circular design problem which exist in pure-feedback systems is overcome. A stability analysis is given which shows that our control law can guarantee the uniformly ultimate boundedness of the solution of the closed-loop system, and make the tracking error arbitrarily small. Moreover, the proposed control design scheme can also be directly applied to the strict-feedback nonlinear systems with arbitrary uncertainty.

[1]  Dan Wang,et al.  Neural network based adaptive dynamic surface control for nonlinear systems in strict-feedback form , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[2]  Shuzhi Sam Ge,et al.  Adaptive NN control of uncertain nonlinear pure-feedback systems , 2002, Autom..

[3]  Dan Wang,et al.  Adaptive neural network control for a class of uncertain nonlinear systems in pure-feedback form , 2002, Autom..

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

[5]  Swaroop Darbha,et al.  Dynamic surface control for a class of nonlinear systems , 2000, IEEE Trans. Autom. Control..

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

[7]  P. P. Yip,et al.  Adaptive dynamic surface control : a simplified algorithm for adaptive backstepping control of nonlinear systems , 1998 .

[8]  Shuzhi Sam Ge,et al.  Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form , 2008, Autom..

[9]  A. Isidori,et al.  Adaptive control of linearizable systems , 1989 .

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

[11]  I. Kanellakopoulos,et al.  Robustness of Adaptive Nonlinear Control Under an Extended Matching Condition , 1989 .

[12]  J. C. Gerdes,et al.  Dynamic surface control of nonlinear systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[13]  Dan Wang,et al.  Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form , 2005, IEEE Transactions on Neural Networks.

[14]  Shuzhi Sam Ge,et al.  An ISS-modular approach for adaptive neural control of pure-feedback systems , 2006, Autom..

[15]  Frank L. Lewis,et al.  Multilayer neural-net robot controller with guaranteed tracking performance , 1996, IEEE Trans. Neural Networks.

[16]  Shuzhi Sam Ge,et al.  Adaptive neural network control for strict-feedback nonlinear systems using backstepping design , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[17]  Kwanghee Nam,et al.  A model reference adaptive control scheme for pure-feedback nonlinear systems , 1987, 1987 American Control Conference.

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

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

[20]  Frank L. Lewis,et al.  Robust backstepping control of nonlinear systems using neural networks , 2000, IEEE Trans. Syst. Man Cybern. Part A.

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

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

[23]  Ioannis Kanellakopoulos,et al.  ROBUSTNESS OF ADAPTIVE NONLINEAR CONTROL UNDER AN EXTENDED MATCHING CONDITION1 , 1990 .