Optimal linear estimation for continuous stochastic systems with random observation delays

Authors

  • Chunyan Han,

    1. School of Control Science and Engineering, Shandong University, Jinan, Shandong, China
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    • Chunyan Han, School of Control Science and Engineering, University of Jinan, Jinan 250022, Shandong, China.

  • Huanshui Zhang,

    Corresponding author
    • School of Control Science and Engineering, Shandong University, Jinan, Shandong, China
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  • Gang Feng

    1. Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong
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    • Gang Feng, Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong.


Huanshui Zhang, School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, China.

E-mail: hszhang@sdu.edu.cn

SUMMARY

This paper is concerned with the linear minimum mean square error estimation for Itô-type differential equation systems with random delays, where the delay process is modeled as a finite-state Markov chain. By first introducing a set of equivalent delay-free observations and then defining two reorganized Markov chains, the estimation problem of random delayed systems is reduced to the one of delay-free Markov jump linear systems. The estimator is derived by using the innovation analysis method based on the Itô differential formula. And the analytical solution to this estimator is given in terms of two Riccati differential equations that are of finite dimensions. Conditions for existence, uniqueness, and stability of the steady-state optimal estimator are studied for time-invariant cases. In this case, the obtained estimator is very easy to implement, and all calculation can be performed off line, leading to a linear time-invariant estimator. Copyright © 2011 John Wiley & Sons, Ltd.

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