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