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Output-feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance. (English) Zbl 0948.93053

Summary: We address the class of stochastic output-feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori. This problem is analogous to deterministic disturbance attenuation problems. We first design a controller which guarantees that the solutions converge (in probability) to a residual set proportional to the unknown bound on the covariance. Then, for the case of a vanishing noise vector field, we design an adaptive controller which, besides global stability in probability, guarantees regulation of the state of the plant to zero with probability one.

MSC:

93D21 Adaptive or robust stabilization
93E15 Stochastic stability in control theory
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