Design of probabilistic $ l_2-l_\infty $ filter for uncertain Markov jump systems with partial information of the transition probabilities

Liqiang Jin; Yanqing Liu; Yanyan Yin; Kok Lay Teo; Fei Liu

doi:10.3934/jimo.2021070

Article Contents

2022, Volume 18, Issue 4: 2335-2349. Doi: 10.3934/jimo.2021070

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Design of probabilistic $ l_2-l_\infty $ filter for uncertain Markov jump systems with partial information of the transition probabilities

1.
Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, China
2.
School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, Western Australia, 6102, Australia
3.
School of Mathematical Sciences, Sunway University, Kuala Lumpur 47500, Malaysia
4.
Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin, China

^* Corresponding author: Fei Liu
^* Corresponding author: Fei Liu

Received: December 2020

Revised: February 2021

Early access: April 2021

Published: July 2022

The first author is supported in part by the National Natural Science Foundation of China under grant nos. 61773011, 61773183, the Ministry of Education of China under the 111 Project B12018 and Curtin Fellowship

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Abstract

In this paper, the problem of $ l_2-l_\infty $ probabilistic filtering for uncertain Markov jump systems with partial information of the transition probabilities is studied, where the uncertainties are caused by randomly changing interior parameters. Combining the original system and the filtering system, an augmented error system is proposed. Some concepts of probability theory are introduced to handle the uncertainties. Due to the complicated structure of real practical systems, only partial information on the transition probabilities are available. In this paper, by using Lyapunov functional method and probability theory, linear matrix inequalities (LMIs) type of sufficient conditions are derived. Based on these sufficient conditions, a probability filter is constructed such that the augmented error system with partial information of the transition probabilities is stochastically stable with a given confidence level and satisfying an $ l_2-l_\infty $ performance index. Furthermore, the gain matrices of the filter are obtained through the introduction of slack matrices. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Keywords:

Probabilistic filtering,
partial information of the transition probabilities,
uncertainties,
probability theory,
linear matrix inequalities (LMIs).

Mathematics Subject Classification: Primary: 93E11, 93E03; Secondary: 37H05.

Citation:

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Figure 1. The system mode trajectory

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Figure 2. The system states curve

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Figure 3. The filtering system state

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Figure 4. The error response curve

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