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

Published online by Cambridge University Press:  20 August 2008

Shuping Tan  and
Ji-Feng Zhang
Shuping Tan
Affiliation:
National Laboratory of Space Intelligent Control, Beijing Institute of Control Engineering, P.O. Box 2729, Beijing 100190, P. R. China. sptan@amss.ac.cn
Ji-Feng Zhang
Affiliation:
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China. jif@iss.ac.cn
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Abstract

This paper is concerned with the sampled-data based adaptivelinear quadratic (LQ) control of hybrid systems with bothunmeasurable Markov jump processes and stochastic noises.By the least matching error estimation algorithm, parameter estimatesare presented. By a double-step (DS) sampling approach and the certaintyequivalence principle, a sampled-data based adaptive LQ control isdesigned. The DS-approach is characterized by a comparatively largeestimation step for parameter estimation and a sufficient small controlstep for control updating. Under mild conditions, the closed-loop systemis shown to be stable. It is found that the key factor determining theperformance index is the estimation step rather than the control step.When the estimation step becomes too small, the system performance willbecome worse. When the estimation step is fixed, the system performancecan indeed be improved by reducing the control step, but cannot reachthe optimal value. The index difference between the sampled-data basedadaptive LQ control and the conventional LQ optimal control is asymptoticallybounded by a constant depending on the estimation step and the prioriinformation of the parameter set.

Keywords

Sampling control systemMarkov jump parameteradaptive controldouble-step approachstochastic noiseleast matching errorestimation
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 4 , October 2009 , pp. 969 - 993
Copyright
© EDP Sciences, SMAI, 2008

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