Reliable Control of Fuzzy Singularly Perturbed Systems and Its Application to Electronic Circuits

In this paper, the reliable control problem of nonlinear singularly perturbed systems subject to random actuator faults is studied. A Takagi-Sugeno fuzzy model is utilized to describe the nonlinear plant, and a Markov chain with partly unknown transition probabilities is adopted to characterize the...

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Bibliographic Details
Published inIEEE transactions on circuits and systems. I, Regular papers Vol. 65; no. 10; pp. 3519 - 3528
Main Authors Wang, Yueying, Shi, Peng, Yan, Huaicheng
Format Journal Article
LanguageEnglish
Published New York IEEE 01.10.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Actuators
Circuit design
Circuits
Control systems
Electronic circuits
Fuzzy control
fuzzy singular-perturbation-parameter-dependent Markovian Lyapunov function
Fuzzy systems
Liapunov functions
Lyapunov methods
Markov analysis
Markov chains
Markov processes
Nonlinear control
Nonlinear systems
partly unknown transition probabilities
reliable control
Search algorithms
Singularly perturbed systems
Takagi-Sugeno fuzzy model
Takagi-Sugeno model
Transition probabilities
Upper bounds
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Summary:In this paper, the reliable control problem of nonlinear singularly perturbed systems subject to random actuator faults is studied. A Takagi-Sugeno fuzzy model is utilized to describe the nonlinear plant, and a Markov chain with partly unknown transition probabilities is adopted to characterize the random behaviors of the actuator faults, in contrast with the existing fault modes in which all the transition probabilities are required to be known. Combining the utilization of a novel fuzzy singular-perturbation-parameter-dependent Markovian Lyapunov function with the introduction of the slack matrix variable, sufficient conditions on the existence of the reliable fuzzy controller are presented, which are dependent on the upper bounds on the time derivatives of membership functions. A search algorithm is provided to obtain the maximum stabilization bound. Moreover, conditions based on single Lyapunov function are also established. The effectiveness and the applicability of the proposed new design technique are verified by an example of an electronic circuit system.
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ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2018.2834481