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Stochastic nonlinear stabilization. I: A backstepping design. (English) Zbl 0902.93049
Summary: While the current robust nonlinear control toolbox includes a number of methods for systems affine in deterministic bounded disturbances, the problem when the disturbance is an unbounded stochastic noise has hardly been considered. We present a control design which achieves global asymptotic (Lyapunov) stability in probability for a class of strict-feedback nonlinear continuous-time systems driven by white noise. In a companion paper, we develop inverse optimal control laws for general stochastic systems affine in the noise input, and for strict-feedback systems. A reader of this paper needs no prior familiarity with techniques of stochastic control.

93C99 Model systems in control theory
93E15 Stochastic stability in control theory
93D15 Stabilization of systems by feedback
Full Text: DOI
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