A novel-designed fuzzy logic control structure for control of distinct chaotic systems
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ORIGINAL ARTICLE
A novel‑designed fuzzy logic control structure for control of distinct chaotic systems Shih‑Yu Li1 · Lap‑Mou Tam2,3 · Hsien‑Keng Chen4 · Chin‑Sheng Chen5 Received: 11 August 2019 / Accepted: 7 April 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, a Lyapunov-based fuzzy logic control (FLC) system is developed for controlling of complicated as well as distinct nonlinear systems. According to Lyapunov Stability Theory, a candidate Lyapunov function with simple quadratic form is designed. Via constructing the fuzzy IF–THEN rules through referencing the statuses of errors states and error derivatives in each sub-space of the Lyapunov function derivatives, the proposed structure of FLC system is able to appropriately as well as flexibly adjust the control forces with minimum magnitude compensating the nonlinear systems in real-time. In addition, the designed FLC system can be applied to different kinds of control systems without further information and operation experience. Two nonlinear systems with distinct structures, classical Lorentz system and Mathieu-van der Pol system, are illustrated for simulation examples. In comparison of the previous research work, the simulation results reveal the effectiveness, flexibility and convenient-design of the proposed method. Keywords Fuzzy logic control · Nonlinear systems · Lyapunov stability theory
1 Introduction Nonlinear dynamics, commonly called the chaos theory [1], changes the scientific way of looking at the dynamics of natural and social systems, which has been intensively studied over the past several decades. The phenomenon of chaotic system has attracted widespread attention amongst various kinds of fields, such as mathematicians, physicists, engineers, bio-mechanics and the rest. The applications of chaotic system have also been extensively studied in many fields, such as fault detections, power converters, * Shih‑Yu Li [email protected] 1
Graduate Institute of Manufacturing Technology, National Taipei University of Technology, Taipei, Taiwan, ROC
2
Institute for the Development and Quality, Macau, Macao, China
3
Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Macao, China
4
Department of Mechanical Engineering, Hsiuping University of Science and Technology, Taichung, Taiwan, ROC
5
Graduate Institute of Automation Technology, National Taipei University of Technology, Taipei, Taiwan, ROC
information processing, secure communications, system control, etc. [2–10]. The concept of fuzzy logic is proposed by L. A. Zadeh in 1965 [11], which has received much attention as a powerful tool for interdisciplinary applications, such as fuzzy modeling [12–17], fault diagnosis [18–20], uncertainty tracing [21–24], fuzzy logic control [25–28], etc. Fuzzy logic control (FLC) system is a conspicuous and successful branch of automation and control theory, the concept of fuzzy logic control is to utilize the qualitative knowledge of a system to des
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