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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) |

### Keywords:

stochastic nonlinear systems; Markovian jump systems; adaptive control; almost sure asymptotic stability
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\textit{G. L. Wang} and \textit{Q. L. Zhang}, Int. J. Adapt. Control Signal Process. 26, No. 9, 848--860 (2012; Zbl 1274.93279)

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