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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.
93C99Control systems, guided systems
93E15Stochastic stability
93D15Stabilization of systems by feedback