Output-feedback stochastic nonlinear stabilization

The authors present the first result on global output-feedback stabilization (in probability) for stochastic nonlinear continuous-time systems. The class of systems that they consider is a stochastic counterpart of the broadest class of deterministic systems for which globally stabilizing controllers are currently available. Their controllers are "inverse optimal" and possess an infinite gain margin. A reader of the paper needs no prior familiarity with techniques of stochastic control.

[1]  R. Freeman,et al.  Robust Nonlinear Control Design: State-Space and Lyapunov Techniques , 1996 .

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

[3]  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).

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

[5]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

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

[7]  X. Mao Stability of Stochastic Differential Equations With Respect to Semimartingales , 1991 .

[8]  H. Khalil Adaptive output feedback control of nonlinear systems represented by input-output models , 1996, IEEE Trans. Autom. Control..

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

[10]  L. Praly,et al.  Stabilization by output feedback for systems with ISS inverse dynamics , 1993 .

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

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

[13]  A. Teel,et al.  Tools for Semiglobal Stabilization by Partial State and Output Feedback , 1995 .

[14]  Riccardo Marino,et al.  Nonlinear control design: geometric, adaptive and robust , 1995 .

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

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

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

[18]  L. Collatz,et al.  Differential equations: An introduction with applications , 1986 .

[19]  M. Jankovic Adaptive nonlinear output feedback tracking with a partial high-gain observer and backstepping , 1997, IEEE Trans. Autom. Control..

[20]  P. Florchinger Lyapunov-like techniques for stochastic stability , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[21]  U. Haussmann,et al.  Singular Optimal Stochastic Controls II: Dynamic Programming , 1995 .

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

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

[24]  U. Haussmann,et al.  Singular Optimal Stochastic Controls I: Existence , 1995 .

[25]  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..

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

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