Adaptive output-feedback control for stochastic nonlinear systems with zero dynamics

A class of stochastic nonlinear systems with unknown bounded parameters and zero dynamics are considered in this paper. By a series of coordinate changes, the original system is re-parameterized, which is suit for using the reduced-order observer and 1-dimension adaptive law to reduce the dynamic order of closed-loop system. In adaptive backstepping design, the quadratic and the quartic Lyapunov functions are presented simultaneously to reduce the static order of nonlinearities. It is shown that all the solutions of the closed-loop system are regulated to an arbitrarily small neighborhood of the origin in probability. Due to the order reduction of the controller, the design scheme in this paper has more practical values. A simulation example demonstrates the control scheme.

[1]  Eduardo Sontag.  A universal construction of Artstein's theorem on nonlinear stabilization , 1989 .

[2]  P. Florchinger.  A universal formula for the stabilization of control stochastic differential equations , 1993 .

[3]  P. Florchinger.  Lyapunov-Like Techniques for Stochastic Stability , 1995 .

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

[5]  P. Florchinger.  Feedback Stabilization of Affine in the Control Stochastic Differential Systems by the Control Lyapunov Function Method , 1997 .

[6]  M. Krstić,et al.  Stochastic nonlinear stabilization—II: inverse optimality , 1997 .

[7]  T. Basar,et al.  Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[8]  H. Deng,et al.  Stochastic Nonlinear Stabilization|part I: a Backstepping Design Submitted to Systems and Control Letters , 1997 .

[9]  M. Krstić,et al.  Stochastic nonlinear stabilization—I: a backstepping design , 1997 .

[10]  Miroslav Krstic,et al.  Stabilization of Nonlinear Uncertain Systems , 1998 .

[11]  Zhong-Ping Jiang,et al.  A combined backstepping and small-gain approach to adaptive output feedback control , 1999, Autom..

[12]  Zhong-Ping Jiang,et al.  A unifying framework for global regulation via nonlinear output feedback , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[13]  Zhong-Ping Jiang,et al.  A unifying framework for global regulation via nonlinear output feedback: from ISS to iISS , 2004, IEEE Transactions on Automatic Control.

[14]  Ji-Feng Zhang,et al.  Reduced-order observer-based control design for nonlinear stochastic systems , 2004, Syst. Control. Lett..

[15]  Wu Zhao.  The Reduced-order Design of Robust Adaptive Backstepping Controller , 2005 .

[16]  ZHANGSi－ying,et al.  The Reduced-order Design of Robust Adaptive Backstepping Controller , 2005 .

[17]  Xue-Jun Xie,et al.  Stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function , 2006 .

[18]  Yungang Liu,et al.  Output feedback stabilization for stochastic nonlinear systems in observer canonical form with stable zero-dynamics , 2007, Science in China Series : Information Sciences.