Adaptive control of stochastic nonlinear systems with Markovian switching. (English) Zbl 1274.93279

Wang, G. L.; Zhang, Q. L.

Int. J. Adapt. Control Signal Process. 26, No. 9, 848-860 (2012).

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)

Keywords:

stochastic nonlinear systems; Markovian jump systems; adaptive control; almost sure asymptotic stability

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