Direct adaptive neural control of completely non-affine pure-feedback nonlinear systems with small-gain approach

In this paper, direct adaptive neural tracking control is proposed for a class of completely non-affine pure-feedback nonlinear systems with only one mild assumption on affine terms, which are obtained using implicit function theorem and mean value theorem. To effectively remove the restriction of the upper bound on the affine terms, a smooth function is introduced to compensate the interconnected term of the former step in backstepping design. The proposed control scheme can not only guarantee the boundedness of all the signals in the closed-loop system and the tracking performance, but also provide a simple and effective way for controlling non-affine pure-feedback systems with a mild assumption. Simulation studies are given to demonstrate the effectiveness of the proposed scheme.

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

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

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

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

[5]  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).

[6]  Shuzhi Sam Ge,et al.  Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems , 2002, Proceedings of the 4th World Congress on Intelligent Control and Automation (Cat. No.02EX527).

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

[8]  F. J. Narcowich,et al.  Persistency of Excitation in Identification Using Radial Basis Function Approximants , 1995 .

[9]  A. Teel,et al.  Singular perturbations and input-to-state stability , 1996, IEEE Trans. Autom. Control..

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

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

[12]  T. Apostol.  Mathematical Analysis , 1957 .

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

[14]  A. Ferrara,et al.  Control of a Class of Mechanical Systems With Uncertainties Via a Constructive Adaptive/Second Order VSC Approach , 2000 .

[15]  Bing Chen,et al.  Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients , 2008, Inf. Sci..

[16]  Bing Chen,et al.  Adaptive Neural Control for a Class of Perturbed Strict-Feedback Nonlinear Time-Delay Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[17]  Shuzhi Sam Ge,et al.  An ISS-modular approach for neural control of pure-feedback systems , 2002 .

[18]  Eduardo Sontag,et al.  New characterizations of input-to-state stability , 1996, IEEE Trans. Autom. Control..

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

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

[21]  Shuzhi Sam Ge,et al.  Adaptive neural control of uncertain MIMO nonlinear systems , 2004, IEEE Transactions on Neural Networks.

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

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

[24]  R. Lozano,et al.  (Almost) exact path tracking control for an autonomous helicopter in hover manoeuvres , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[25]  S.S. Ge,et al.  Adaptive Neural Control of Non-Affine Pure-Feedback Systems , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..