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Adaptive control of stochastic nonlinear systems with Markovian switching. (English) Zbl 1274.93279
Summary: This paper is concerned with the problem of adaptive control for a class of stochastic nonlinear systems with Markovian switching, where the upper bounds of nonlinearities of stochastic Markovian jump systems are assumed to be unknown. Firstly, an adaptation law is developed to estimate these unknown parameters. Then, a class of adaptive state feedback controller is proposed such that not only the estimated errors are bounded almost surely but also, the states of the resulting closed-loop system are asymptotically stable almost surely. Finally, a numerical example is given to show the validity of the results.

MSC:
93E15 Stochastic stability in control theory
93D20 Asymptotic stability in control theory
93C40 Adaptive control/observation systems
93C10 Nonlinear systems in control theory
60J75 Jump processes (MSC2010)
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