Stochastic Nonlinear Stabilization|part I: a Backstepping Design Submitted to Systems and Control Letters

While the current robust nonlinear control toolbox includes a number of methods for systems aane in a deterministic bounded disturbances, the problem when the disturbance is unbounded stochastic noise has hardly been considered. We present a control design which achieves global asymptotic (Lyapunov) stability in probability for a class of strict-feedback nonlinear continuous-time systems driven by white noise. In a companion paper, we develop inverse optimal control laws for general stochastic systems aane in the noise input, and for strict-feedback systems. A reader of this paper needs no prior familiarity with techniques of stochastic control.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  B. Øksendal.  Stochastic differential equations : an introduction with applications , 1987 .

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

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

[5]  T. Runolfsson.  The equivalence between infinite-horizon optimal control of stochastic systems with exponential-of-integral performance index and stochastic differential games , 1994, IEEE Trans. Autom. Control..

[6]  S.,et al.  Risk-Sensitive Control and Dynamic Games for Partially Observed Discrete-Time Nonlinear Systems , 1994 .

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

[8]  Tamer Başar,et al.  H1-Optimal Control and Related Minimax Design Problems , 1995 .

[9]  H. Nagai.  Bellman equations of risk sensitive control , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

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

[11]  Randy A. Freeman,et al.  Robust Nonlinear Control Design , 1996 .

[12]  T. Basar,et al.  H∞-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach , 1996, IEEE Trans. Autom. Control..

[13]  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).