Pareto optimal filter design with hybrid $ H_{2} /H_{\infty} $ optimization

Xiaoyu Ren; Ting Hou; Xiaoyu Ren; Ting Hou

doi:10.3934/mmc.2023008

Mathematical Modelling and Control

2023, Volume 3, Issue 2: 80-87. doi: 10.3934/mmc.2023008

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Research article

Pareto optimal filter design with hybrid $ H_{2} /H_{\infty} $ optimization

Xiaoyu Ren ,
Ting Hou ^,

School of Mathematics and Statistics, Shandong Normal University, Jinan 250000, Shandong Province, China

Received: 21 December 2023 Revised: 26 February 2023 Accepted: 05 March 2023 Published: 23 March 2023

In this article, we study the Pareto optimal $ H_{2} $ /$ H_{\infty} $ filter design problem for a generalization of discrete-time stochastic systems. By constructing the estimation equation of the given systems with the estimated signal, a filter error estimation system is obtained. The aim is to obtain a gain matrix $ K^{\star} $ that optimizes both performance indicators we set. To deal with this problem, two different upper bounds for two performance indicators are given respectively. The optimal problem therefore is transformed into a Pareto optimal problem with linear matrix inequalities ($ LMIs $) which can be addressed through the $ LMI $ toolbox in $ MATLAB $.
- $ {LMIs} $,
- $ H_{2}/H_{\infty} $ filter,
- Pareto optimality solutions,
- multi-objective problem
Citation: Xiaoyu Ren, Ting Hou. Pareto optimal filter design with hybrid $ H_{2} /H_{\infty} $ optimization[J]. Mathematical Modelling and Control, 2023, 3(2): 80-87. doi: 10.3934/mmc.2023008

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Abstract

In this article, we study the Pareto optimal $ H_{2} $ /$ H_{\infty} $ filter design problem for a generalization of discrete-time stochastic systems. By constructing the estimation equation of the given systems with the estimated signal, a filter error estimation system is obtained. The aim is to obtain a gain matrix $ K^{\star} $ that optimizes both performance indicators we set. To deal with this problem, two different upper bounds for two performance indicators are given respectively. The optimal problem therefore is transformed into a Pareto optimal problem with linear matrix inequalities ($ LMIs $) which can be addressed through the $ LMI $ toolbox in $ MATLAB $.

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