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IMA Journal of Mathematical Control and Information Advance Access originally published online on August 2, 2006
IMA Journal of Mathematical Control and Information 2007 24(2):219-234; doi:10.1093/imamci/dnl024
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Lower-order state-space self-tuning control for a stochastic chaotic hybrid system

Tseng-Hsu Chien1, Jason Sheng Hong Tsai**,1, Shu-Mei Guo2 and Guanrong Chen3

1 Control System Laboratory, Department of Electrical Engineering, National Cheng-Kung University, Tainan 701, Taiwan, Republic of China, 2 Department of Computer Science and Information Engineering, National Cheng-Kung University, Tainan 701, Taiwan, Republic of China, 3 Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, People's Republic of China

** Email: shtsai{at}mail.ncku.edu.tw


  Abstract

In this paper, subject to acceptable closed-loop performance, an effective lower-order tuner for a stochastic chaotic hybrid system is designed using the observer/Kalman filter identification (OKID) method, in which the system state in a general coordinate form is transformed to one in an observer form. The OKID method is a time-domain technique that identifies a discrete input–output map by using known input–output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm. Moreover, it provides a lower-order realization of the tracker, with computationally effective initialization, for on-line "auto-regressive moving average process with exogenous model" -based identification and a lower-order state-space self-tuning control technique. Finally, the chaotic Chen's system is used as an illustrative example to demonstrate the effectiveness of the proposed methodology.

Keywords: self-tuning control; stochastic system; chaotic system; orbit tracker; Markov parameters.


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