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Zbl 1008.93068
Deng, Hua; Krstić, Miroslav; Williams, Ruth J.
Stabilization of stochastic nonlinear systems driven by noise of unknown covariance. (English)
[J] IEEE Trans. Autom. Control 46, No.8, 1237-1253 (2001). ISSN 0018-9286

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.
[Klaus Ehemann (Karlsruhe)]

MSC 2000:: *93E15 Stochastic stability
93D21 Adaptive and robust stabilization
93D30 Scalar and vector Lyapunov functions
91A15 Stochastic games

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

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