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Design of Optimal Controllers for Unknown Dynamic Systems through the Nelder–Mead Simplex Method

Author

Listed:
  • Hsun-Heng Tsai

    (Department of Biomechatronics Engineering, National Pingtung University of Science and Technology, Pingtung 91201, Taiwan)

  • Chyun-Chau Fuh

    (Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan)

  • Jeng-Rong Ho

    (Department of Mechanical Engineering, National Central University, Taoyuan 320317, Taiwan)

  • Chih-Kuang Lin

    (Department of Mechanical Engineering, National Central University, Taoyuan 320317, Taiwan)

Abstract

This paper presents an efficient method for designing optimal controllers. First, we established a performance index according to the system characteristics. In order to ensure that this performance index is applicable even when the state/output of the system is not within the allowable range, we added a penalty function. When we use a certain controller, if the state/output of the system remains within the allowable range within the preset time interval, the penalty function value is zero. Conversely, if the system state/output is not within the allowable range before the preset termination time, the experiment/simulation is terminated immediately, and the penalty function value is proportional to the time difference between the preset termination time and the time at which the experiment was terminated. Then, we used the Nelder–Mead simplex method to search for the optimal controller parameters. The proposed method has the following advantages: (1) the dynamic equation of the system need not be known; (2) the method can be used regardless of the stability of the open-loop system; (3) this method can be used in nonlinear systems; (4) this method can be used in systems with measurement noise; and (5) the method can improve design efficiency.

Suggested Citation

  • Hsun-Heng Tsai & Chyun-Chau Fuh & Jeng-Rong Ho & Chih-Kuang Lin, 2021. "Design of Optimal Controllers for Unknown Dynamic Systems through the Nelder–Mead Simplex Method," Mathematics, MDPI, vol. 9(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:2013-:d:620033
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    References listed on IDEAS

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    1. C.J. Price & I.D. Coope & D. Byatt, 2002. "A Convergent Variant of the Nelder–Mead Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 5-19, April.
    2. Chao Liu & Weiqiang Zhao & Jie Li, 2020. "Gain Scheduling Output Feedback Control for Vehicle Path Tracking Considering Input Saturation," Energies, MDPI, vol. 13(17), pages 1-19, September.
    3. Xu, Shuhui & Wang, Yong & Wang, Zhi, 2019. "Parameter estimation of proton exchange membrane fuel cells using eagle strategy based on JAYA algorithm and Nelder-Mead simplex method," Energy, Elsevier, vol. 173(C), pages 457-467.
    4. Ali Tavasoli & Vali Enjilela, 2017. "Active disturbance rejection and Lyapunov redesign approaches for robust boundary control of plate vibration," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(8), pages 1656-1670, June.
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    Cited by:

    1. Ilia Beloglazov & Kirill Krylov, 2022. "An Interval-Simplex Approach to Determine Technological Parameters from Experimental Data," Mathematics, MDPI, vol. 10(16), pages 1-12, August.

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