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

Hsun-Heng Tsai, Chyun-Chau Fuh, Jeng-Rong Ho and Chih-Kuang Lin
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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

Mathematics, 2021, vol. 9, issue 16, 1-14

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.

Keywords: optimal control; penalty function; performance index; N–M simplex method; inverted pendulum (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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