Trigonometric RBF neural robust controller design for a class of nonlinear system with linear input unmodeled dynamics

Considered both the situation with unknown control function matrices and the situation with linear unmodeled input dynamics, adaptive neural robust controller was designed by using adaptive backstepping method for a class of multi-input to multi-output nonlinear systems which could be turned to ''standard block control type''. It was proved by constructing Lyapunov function step by step that all signals of the system are bounded and exponentially converge to the neighborhood of the origin globally. And by adopting the trigonometric function as basis function, the input need not be force to between -1 and 1, and there is no need to choose the centre of basis function which reduced the difficulty of doing simulation and made the neural net work more practical. And the variable structure control is adopt to eliminate the error of approximation. Also the method of differential reconstruction of neural network is used to increase the damp of neural network and it makes the system more stable. Finally, simulation study is given to demonstrate that the proposed method is effective and the known information of system was made use of as maximally as possible by introducing the PID control.

[1]  Riccardo Marino,et al.  An extended direct scheme for robust adaptive nonlinear control , 1991, Autom..

[2]  Zhihua Qu,et al.  Robust Control of Nonlinear Uncertain Systems Under Generalized Matching Conditions , 1993, 1993 American Control Conference.

[3]  Chen-Chung Liu,et al.  Adaptively controlling nonlinear continuous-time systems using multilayer neural networks , 1994, IEEE Trans. Autom. Control..

[4]  Zhang Youan.  Robust Neural Adaptive Tracking Control for Nonlinear Systems , 2001 .

[5]  Lyle H. Ungar,et al.  Adaptive networks for fault diagnosis and process control , 1990 .

[6]  Zhong-Ping Jiang,et al.  Controlling nonlinear systems with input unmodelled dynamics , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[7]  B Michael.  NEURAL NETWORKS FOR STABLE ADAPTIVE CONTROL OF AIR-TO-AIR MISSILES , 1995 .

[8]  T Poggio,et al.  Regularization Algorithms for Learning That Are Equivalent to Multilayer Networks , 1990, Science.

[9]  Nader Sadegh,et al.  A perceptron network for functional identification and control of nonlinear systems , 1993, IEEE Trans. Neural Networks.

[10]  Hassan K. Khalil,et al.  Adaptive control of a class of nonlinear discrete-time systems using neural networks , 1995, IEEE Trans. Autom. Control..

[11]  Miroslav Krstic,et al.  Stability margins in inverse optimal input-to-state stabilization , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

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

[13]  Petar V. Kokotovic,et al.  Robust nonlinear control of systems with input unmodeled dynamics , 2000 .

[14]  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).

[15]  P. Kokotovic,et al.  Robust control of nonlinear systems with input unmodeled dynamics , 1996, IEEE Trans. Autom. Control..

[16]  Anthony J. Calise,et al.  Nonlinear flight control using neural networks , 1994 .

[17]  Shuzhi Sam Ge,et al.  Direct adaptive neural network control of robots , 1996, Int. J. Syst. Sci..

[18]  Laurent Praly,et al.  Ignored input dynamics and a new characterization of control Lyapunov functions , 1999, 1999 European Control Conference (ECC).

[19]  Miroslav Krstic,et al.  Control of feedback linearizable systems with input unmodeled dynamics , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[20]  Zhong-Ping Jiang,et al.  Robust global stabilization with ignored input dynamics: an input-to-state stability (ISS) small-gain approach , 2001, IEEE Trans. Autom. Control..

[21]  D.A. Handelman,et al.  Theory and development of higher-order CMAC neural networks , 1992, IEEE Control Systems.

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

[23]  Frank L. Lewis,et al.  Neural net robot controller with guaranteed tracking performance , 1995, IEEE Trans. Neural Networks.

[24]  D. Serakos,et al.  Nonlinear controllers for a tail-fin controlled missile , 1993, Proceedings of Southeastcon '93.

[25]  Jesse Leitner.  Helicopter nonlinear control using adaptive feedback linearization , 1995 .

[26]  Andrew R. Barron,et al.  Universal approximation bounds for superpositions of a sigmoidal function , 1993, IEEE Trans. Inf. Theory.

[27]  Neil E. Cotter,et al.  The Stone-Weierstrass theorem and its application to neural networks , 1990, IEEE Trans. Neural Networks.

[28]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[29]  Zhong-Ping Jiang,et al.  A small-gain control method for nonlinear cascaded systems with dynamic uncertainties , 1997, IEEE Trans. Autom. Control..

[30]  Zhong-Ping Jiang,et al.  Small-gain theorem for ISS systems and applications , 1994, Math. Control. Signals Syst..

[31]  P. Kokotovic,et al.  CLF based designs with robustness to dynamic input uncertainties , 1999 .

[32]  Frank L. Lewis,et al.  Multilayer discrete-time neural-net controller with guaranteed performance , 1996, IEEE Trans. Neural Networks.

[33]  Riccardo Marino,et al.  Robust stabilization of feedback linearizable time-varying uncertain nonlinear systems, , 1993, Autom..

[34]  Madan M. Gupta,et al.  Neuro-Control Systems: Theory and Applications , 1993 .

[35]  Donald A. Sofge,et al.  Handbook of Intelligent Control: Neural, Fuzzy, and Adaptive Approaches , 1992 .

[36]  David G. Taylor,et al.  Adaptive Regulation of Nonlinear Systems with Unmodeled Dynamics , 1988, 1988 American Control Conference.

[37]  Yuan Wang,et al.  Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability , 1996, Math. Control. Signals Syst..

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

[39]  Youan Zhang,et al.  Nonlinear adaptive control of uncertain missile systems with input unmodeled dynamics using RBF neural networks , 2002 .

[40]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.