Linear matrix inequality conditions of nonlinear systems by genetic algorithm-based H∞ adaptive fuzzy sliding mode controller

P. C. Chen; C. W. Chen; W. L. Chiang

doi:10.1177/1077546309352826

Linear matrix inequality conditions of nonlinear systems by genetic algorithm-based H_∞ adaptive fuzzy sliding mode controller

P. C. Chen, C. W. Chen, W. L. Chiang

Department of Civil Engineering

Research output: Contribution to journal › Article › peer-review

49 Scopus citations

Abstract

In this paper, the stability analysis of a genetic algorithm-based (GA-based) H_∞ adaptive fuzzy sliding model controller (AFSMC) for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving fuzzy logic control (FLC) rules. Then, FLC rules and the consequent parameter are decided on via a genetic algorithm. After this, we guarantee a new H_∞ tracking performance inequality for the control system. The H_∞ tracking problem is characterized to solve an eigenvalue problem. Next, an AFSMC is proposed to stabilize the system so as to achieve good H_∞ control performance. Lyapunov's direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

Original language	English
Pages (from-to)	163-173
Number of pages	11
Journal	JVC/Journal of Vibration and Control
Volume	17
Issue number	2
DOIs	https://doi.org/10.1177/1077546309352826
State	Published - Feb 2011

Keywords

Adaptive fuzzy sliding mode control
H infinity
Lyapunov direct method

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10.1177/1077546309352826

Cite this

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abstract = "In this paper, the stability analysis of a genetic algorithm-based (GA-based) H∞ adaptive fuzzy sliding model controller (AFSMC) for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving fuzzy logic control (FLC) rules. Then, FLC rules and the consequent parameter are decided on via a genetic algorithm. After this, we guarantee a new H∞ tracking performance inequality for the control system. The H∞ tracking problem is characterized to solve an eigenvalue problem. Next, an AFSMC is proposed to stabilize the system so as to achieve good H∞ control performance. Lyapunov's direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality problem. Finally, a numerical simulation is provided to demonstrate the control methodology.",

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AB - In this paper, the stability analysis of a genetic algorithm-based (GA-based) H∞ adaptive fuzzy sliding model controller (AFSMC) for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving fuzzy logic control (FLC) rules. Then, FLC rules and the consequent parameter are decided on via a genetic algorithm. After this, we guarantee a new H∞ tracking performance inequality for the control system. The H∞ tracking problem is characterized to solve an eigenvalue problem. Next, an AFSMC is proposed to stabilize the system so as to achieve good H∞ control performance. Lyapunov's direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

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