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.

中文翻译：

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一种新颖的模糊逻辑控制结构，用于控制不同的混沌系统

在本文中，开发了基于Lyapunov的模糊逻辑控制（FLC）系统，用于控制复杂以及截然不同的非线性系统。根据李雅普诺夫稳定性理论，设计了具有简单二次形式的候选李雅普诺夫函数。通过参考Lyapunov函数导数的每个子空间中的错误状态和错误导数的状态来构造模糊IF–THEN规则，所提出的FLC系统结构能够以最小幅度适当地且灵活地调整控制力实时补偿非线性系统。此外，所设计的FLC系统无需进一步的信息和操作经验即可应用于各种控制系统。两个具有不同结构的非线性系统，经典的Lorentz系统和Mathieu-van der Pol系统，给出了仿真示例。与以往的研究工作相比，仿真结果表明了该方法的有效性，灵活性和便捷性。