Stabilization of stochastic nonlinear systems driven by noise of unknown covariance. (English) Zbl 1008.93068

Deng, Hua; Krstić, Miroslav; Williams, Ruth J.

IEEE Trans. Autom. Control 46, No. 8, 1237-1253 (2001).

This paper regards a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded in expectation by a monotone function of the supremum of the covariance of noise. It begins with a set of new global stochastic Lyapunov theorems. For an exemplary class of stochastic strict-feedback systems an adaptive stabilization scheme is developed. Further, a control Lyapunov function formula for stochastic disturbance attenuation is introduced. Finally, optimality and the solution of a differential game problem with the control and the noise covariance as opposite players are treated.

Reviewer: Klaus Ehemann (Karlsruhe)

MSC:

93E15	Stochastic stability in control theory
93D21	Adaptive or robust stabilization
93D30	Lyapunov and storage functions
91A15	Stochastic games, stochastic differential games

Keywords:

global stochastic Lyapunov theorems; adaptive stabilization; control Lyapunov function; stochastic disturbance attenuation; differential game; noise covariance