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Intelligent Controls for Switched Fuzzy Systems: Synthesis via Nonstandard Lyapunov Functions

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Recent Contributions in Intelligent Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 657))

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Abstract

This paper investigates the synthesis of intelligent control algorithms for switched fuzzy systems by employing nonstandard Lyapunov functions and combined techniques. Controlled plants are assumed nonlinear and to be represented by certain specific T–S fuzzy models. In one of case studies, a two-layer multiple Lyapunov functions approach is developed that yields a stability condition for uncontrolled switched fuzzy systems and a stabilization condition for closed-loop switched fuzzy systems under a switching law. State feedback controllers with the time derivative information of membership functions are simultaneously designed. In another case, Lyapunov functions approach is developed that yields a non-fragile guaranteed cost optimal stabilization in closed-loop for switched fuzzy systems provided a certain convex combination condition is fulfilled. Solutions in both cases are found in terms of derived linear matrix inequalities, which are solvable on MATLAB platform. In another case, a single Lyapunov function approach is developed to synthesize intelligent control in which a designed switching law handles stabilization of unstable subsystems while the accompanied non-fragile guaranteed cost control law ensures the optimality property. Also, an algorithm is proposed to carry out feasible convex combination search in conjunction with the optimality of intelligent control. It is shown that, when an optimality index is involved, the intelligent controls are capable of tolerating some uncertainty not only in the plant but also in the controller implementation. For both cases of intelligent control synthesis solutions illustrative examples along with the respective simulation results are given to demonstrate the effectiveness and the achievable nonconservative performance of those intelligent controls in closed loop system architectures.

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Acknowledgments

This research cooperation was generously supported in part by the NSFC of the P.R. of China (grants 61174073 and 908160028) and by the Ministry of Education & Science of the Republic Macedonia (grant 14-3145/1-17.12.2007), and also by the Fund for Science of Dogus University, Istanbul, Turkish Republic. These respective supports are gratefully acknowledged by the authors, respectively.

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Authors and Affiliations

  1. Signal State Key Laboratory of Synthetic Automation for Process Industries, College of Information Science & Engineering, Northeastern University, Shenyang, 110819, Liaoning, People’s Republic of China

    Jinming Luo

  2. Departments of Computer and of Control & Automation Engineering, School of Engineering, Dogus University, Acibadem, Istanbul, TR-34722, Turkey

    Georgi M. Dimirovski

  3. Institute of ASE, Faculty of Electrical Eng. & Information Technologies, SS Cyril & Methodius University, Skopje, MK-1000, Republic of Macedonia

    Georgi M. Dimirovski

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  1. Jinming Luo
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Correspondence to Jinming Luo .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Vassil Sgurev

  2. Machine Intelligence Institute, Hagan School of Business, Iona College, New Rochelle, New York, USA

    Ronald R. Yager

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  4. Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

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Luo, J., Dimirovski, G.M. (2017). Intelligent Controls for Switched Fuzzy Systems: Synthesis via Nonstandard Lyapunov Functions. In: Sgurev, V., Yager, R., Kacprzyk, J., Atanassov, K. (eds) Recent Contributions in Intelligent Systems. Studies in Computational Intelligence, vol 657. Springer, Cham. https://doi.org/10.1007/978-3-319-41438-6_8

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  • DOI: https://doi.org/10.1007/978-3-319-41438-6_8

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