Almost Sure Stabilization for Adaptive Controls of Regime-switching LQ Systems with A Hidden Markov Chain

Bernard Bercu 1, 2 Francois Dufour 1, 2 G. George Yin
2 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a hidden Markov chain. Different from previous work on stabilization of adaptive controlled systems with a hidden Markov chain, where average criteria were considered, this work focuses on the almost sure stabilization or sample path stabilization of the underlying processes. Under simple conditions, it is shown that as long as the feedback controls have linear growth in the continuous component, the resulting process is regular. Moreover, by appropriate choice of the Lyapunov functions, it is shown that the adaptive system is stabilizable almost surely. As a by-product, it is also established that the controlled process is positive recurrent.
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Journal articles
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Submitted on : Wednesday, May 20, 2009 - 5:33:14 PM
Last modification on : Thursday, January 11, 2018 - 6:22:11 AM

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  • HAL Id : hal-00386244, version 1
  • ARXIV : 0807.1413

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Bernard Bercu, Francois Dufour, G. George Yin. Almost Sure Stabilization for Adaptive Controls of Regime-switching LQ Systems with A Hidden Markov Chain. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2009, 54, pp.1-25. ⟨hal-00386244⟩

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