The self-adaptive terminal sliding mode synchronization of fractional-order nonlinear chaotic systems is investigated under uncertainty and external disturbance. A novel non-singular terminal sliding surface is proposed and proved to be stable. Based on Lyapunov stability theory, a sliding mode control law is proposed to ensure the occurrence of sliding-mode motion. In addition, two methods of the controller and the self-adaptive rules are used to establish the sliding mode function, and two sufficient conditions for achieving self-adaptive terminal sliding-mode synchronization of fractional-order uncertain nonlinear systems are identified. The results show that designing appropriate control law and sliding-mode surface can achieve self-adaptive terminal sliding mode synchronization of the fractional high-order systems with uncertainty. The effectiveness and applicability of the sliding mode control technique are validated through numerical simulation.

中文翻译：

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分数阶非线性混沌系统终端滑模同步的两种方法

研究了不确定性和外部扰动下分数阶非线性混沌系统的自适应终端滑模同步问题。提出了一种新的非奇异终端滑动面，并证明是稳定的。基于李雅普诺夫稳定性理论，提出了一种滑模控制律来保证滑模运动的发生。此外，利用控制器和自适应规则两种方法建立滑模函数，确定了实现分数阶不确定非线性系统自适应终端滑模同步的两个充分条件。结果表明，设计合适的控制律和滑模面可以实现具有不确定性的分数高阶系统的自适应终端滑模同步。