Adaptive state feedback control for a class of stochastic nonlinear systems

In this paper, tracking problem is studied for a class of stochastic nonlinear systems, which is in strict-feedback form and with unknown parametric nonlinearities. Under the condition of all system states being available for feedback, by employing the stochastic Lyapunov-like theorem and the backstepping design technique, an adaptive state feedback control is developed. The output of the closed-loop system is proven to follow the desired trajectory asymptotically in probability.

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

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

[3]  Tamer Basar,et al.  Decentralized risk-sensitive controller design for strict-feedback systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[4]  Graham C. Goodwin,et al.  A parameter estimation perspective of continuous time model reference adaptive control , 1987, Autom..

[5]  Shuzhi Sam Ge,et al.  Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems , 2003, Autom..

[6]  Tao Zhang,et al.  Stable adaptive control for nonlinear multivariable systems with a triangular control structure , 2000, IEEE Trans. Autom. Control..

[7]  Patrick Florchinger,et al.  Global stabilization of cascade stochastic systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

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

[9]  Miroslav Krstic,et al.  Output-feedback stochastic nonlinear stabilization , 1999, IEEE Trans. Autom. Control..

[10]  S. Ge,et al.  Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems via backstepping , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[11]  Yungang Liu,et al.  Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost , 2003, IEEE Trans. Autom. Control..

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

[13]  S. Ge,et al.  Stable adaptive control for a class of nonlinear systems using a modified Lyapunov function , 1999, IEEE Trans. Autom. Control..

[14]  I. Kanellakopoulos,et al.  Adaptive nonlinear control without overparametrization , 1992 .

[15]  Anuradha M. Annaswamy,et al.  Robust Adaptive Control , 1984, 1984 American Control Conference.

[16]  T. Başar,et al.  Backstepping Controller Design for Nonlinear Stochastic Systems Under a Risk-Sensitive Cost Criterion , 1999 .

[17]  Tamer Basar,et al.  Risk-sensitive adaptive trackers for strict-feedback systems with output measurements , 2002, IEEE Trans. Autom. Control..

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

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

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

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

[22]  R. Khasminskii.  Stochastic Stability of Differential Equations , 1980 .

[23]  Shuzhi Sam Ge,et al.  Adaptive Neural Network Control of Robotic Manipulators , 1999, World Scientific Series in Robotics and Intelligent Systems.

[24]  T. Başar,et al.  Adaptive Controller Design for Tracking and Disturbance Attenuation in Parametric-Strict-Feedback Nonlinear Systems , 1996 .

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

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

[27]  Jing Wang,et al.  Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients , 2003, IEEE Trans. Autom. Control..

[28]  Jin Chaoyong,et al.  Decentralized stabilization of a class of interconnected systems , 2001 .

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

[30]  Shuzhi Sam Ge,et al.  Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).