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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.

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