Double-stepped adaptive control for hybrid systems with unknown Markov jumps and stochastic noises

Issue		ESAIM: COCV Volume 15, Number 4, October-December 2009


Page(s)		969 - 993
DOI		10.1051/cocv:2008057
Published online		20 August 2008

ESAIM: COCV 15 (2009) 969-993
DOI: 10.1051/cocv:2008057

Double-stepped adaptive control for hybrid systems with unknown Markov jumps and stochastic noises

Shuping Tan¹ and Ji-Feng Zhang²

¹ National Laboratory of Space Intelligent Control, Beijing Institute of Control Engineering, P.O. Box 2729, Beijing 100190, P. R. China. sptan@amss.ac.cn
² Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China. jif@iss.ac.cn

Received January 7, 2007. Revised June 9, 2008. Published online August 20, 2008.

Abstract
This paper is concerned with the sampled-data based adaptive linear quadratic (LQ) control of hybrid systems with both unmeasurable Markov jump processes and stochastic noises. By the least matching error estimation algorithm, parameter estimates are presented. By a double-step (DS) sampling approach and the certainty equivalence principle, a sampled-data based adaptive LQ control is designed. The DS-approach is characterized by a comparatively large estimation step for parameter estimation and a sufficient small control step for control updating. Under mild conditions, the closed-loop system is shown to be stable. It is found that the key factor determining the performance index is the estimation step rather than the control step. When the estimation step becomes too small, the system performance will become worse. When the estimation step is fixed, the system performance can indeed be improved by reducing the control step, but cannot reach the optimal value. The index difference between the sampled-data based adaptive LQ control and the conventional LQ optimal control is asymptotically bounded by a constant depending on the estimation step and the priori information of the parameter set.

Mathematics Subject Classification. 93E15, 93E35

Key words: Sampling control system, Markov jump parameter, adaptive control, double-step approach, stochastic noise, least matching error estimation

© EDP Sciences, SMAI 2008

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