IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i11p2482-d1157856.html
   My bibliography  Save this article

Passive Fuzzy Controller Design for the Parameter-Dependent Polynomial Fuzzy Model

Author

Listed:
  • Cheung-Chieh Ku

    (Department of Marine Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 805, Taiwan)

  • Chein-Chung Sun

    (Department of Marine Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 805, Taiwan)

  • Shao-Hao Jian

    (Department of Marine Engineering, National Taiwan Ocean University, Keelung 202, Taiwan)

  • Wen-Jer Chang

    (Department of Marine Engineering, National Taiwan Ocean University, Keelung 202, Taiwan)

Abstract

This paper discusses a passive control issue for Nonlinear Time-Varying (NTV) systems subject to stability and attenuation performance. Based on the modeling approaches of Takagi-Sugeno (T-S) fuzzy model and Linear Parameter-Varying (LPV) model, a Parameter-Dependent Polynomial Fuzzy (PDPF) model is constructed to represent NTV systems. According to the Parallel Distributed Compensation (PDC) concept, a parameter-dependent polynomial fuzzy controller is built to achieve robust stability and passivity of the PDPF model. Furthermore, the passive theory is applied to achieve performance, constraining the disturbance effect on the PDPF systems. To develop the stability criteria, by introducing a parameter-dependent polynomial Lyapunov function, one can derive some stability conditions, which belong to the term of Sum-Of-Squares (SOS) form. Based on the Lyapunov function, two stability criteria are proposed to design the corresponding PDPF controller, such that the NTV system is robustly stable and passive. Finally, two examples are applied to demonstrate the effectiveness of the proposed stability criterion.

Suggested Citation

  • Cheung-Chieh Ku & Chein-Chung Sun & Shao-Hao Jian & Wen-Jer Chang, 2023. "Passive Fuzzy Controller Design for the Parameter-Dependent Polynomial Fuzzy Model," Mathematics, MDPI, vol. 11(11), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2482-:d:1157856
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/11/2482/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/11/2482/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. R. Kavikumar & R. Sakthivel & O. M. Kwon & B. Kaviarasan, 2020. "Faulty actuator-based control synthesis for interval type-2 fuzzy systems via memory state feedback approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(15), pages 2958-2981, November.
    2. Hayato Waki & Maho Nakata & Masakazu Muramatsu, 2012. "Strange behaviors of interior-point methods for solving semidefinite programming problems in polynomial optimization," Computational Optimization and Applications, Springer, vol. 53(3), pages 823-844, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ernest K. Ryu & Yanli Liu & Wotao Yin, 2019. "Douglas–Rachford splitting and ADMM for pathological convex optimization," Computational Optimization and Applications, Springer, vol. 74(3), pages 747-778, December.
    2. Yoshiyuki Sekiguchi & Hayato Waki, 2021. "Perturbation Analysis of Singular Semidefinite Programs and Its Applications to Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 52-72, January.
    3. Jianing Cao & Hua Chen, 2023. "Mathematical Model for Fault Handling of Singular Nonlinear Time-Varying Delay Systems Based on T-S Fuzzy Model," Mathematics, MDPI, vol. 11(11), pages 1-13, June.
    4. Turki Alsuwian & Muhammad Tayyeb & Arslan Ahmed Amin & Muhammad Bilal Qadir & Saleh Almasabi & Mohammed Jalalah, 2022. "Design of a Hybrid Fault-Tolerant Control System for Air–Fuel Ratio Control of Internal Combustion Engines Using Genetic Algorithm and Higher-Order Sliding Mode Control," Energies, MDPI, vol. 15(15), pages 1-23, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2482-:d:1157856. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.