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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.
93E15Stochastic stability
93D21Adaptive or robust stabilization
93D30Scalar and vector Lyapunov functions
91A15Stochastic games