Adaptive stabilization for a class of non-affine non-minimum phase systems using neural networks

For a class of single-input single-output non-affine non-minimum phase nonlinear systems, a neural control synthesis method based on backstepping combined with inverting design is considered. The method reduces the number of steps in designing a backstepping controller compared to previous approaches by seeking a state that stabilizes the unstable internal dynamics. The method does not need a fixed-point assumption nor the boundedness assumption on the time derivative of a control effectiveness term. Using Lyapunov's direct method, it is shown that all the signals of the closed-loop system are uniformly ultimately bounded. Simulation results illustrate the approach

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

[2]  A. Astolfi,et al.  Output feedback stabilization of a class of uncertain nonlinear systems , 2004, Proceedings of the 2004 American Control Conference.

[3]  Alberto Isidori,et al.  Nonlinear Control Systems II , 1999 .

[4]  Tao Zhang,et al.  Stable Adaptive Neural Network Control , 2001, The Springer International Series on Asian Studies in Computer and Information Science.

[5]  Anthony J. Calise,et al.  Adaptive output feedback control of nonlinear systems using neural networks , 2001, Autom..

[6]  Zhong-Ping Jiang,et al.  Output-feedback stabilization of a class of uncertain non-minimum-phase nonlinear systems , 2005, Autom..

[7]  D. Mayne.  Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[8]  A.J. Calise,et al.  Adaptive Control of a Class of Non-Affine Systems using Neural Networks , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[9]  Anthony J. Calise,et al.  Adaptive output feedback control of nonlinear systems using neural networks , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[10]  Anthony M. Bloch,et al.  Nonlinear Dynamical Control Systems (H. Nijmeijer and A. J. van der Schaft) , 1991, SIAM Review.

[11]  Ching-Hung Lee,et al.  Stabilization of nonlinear nonminimum phase systems: adaptive parallel approach using recurrent fuzzy neural network , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[12]  George Leitmann,et al.  A controller for a class of mismatched uncertain systems , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[13]  Martin Corless,et al.  On the necessity of the matching condition in robust stabilization , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.