This paper studies the synchronization of a class of uncertain fractional order (FO) chaotic systems that is applicable in secure communication. A novel hybrid FO controller, based on sliding mode and state feedback techniques combined with fuzzy logic, is developed. The algorithm, derived via the fractional Lyapunov theory, guarantees the stability of the overall system and the convergence of the synchronization errors toward a small residual set. Simulations demonstrate the capability of the proposed control algorithm in secure communications, not only in terms of speed of response, but also by reducing the chattering phenomenon.

中文翻译：

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分数阶滑模和状态反馈控制器的模糊逻辑嵌入，用于不确定分数阶混沌系统的同步

本文研究了一类适用于安全通信的不确定分数阶（FO）混沌系统的同步。基于滑模和状态反馈技术，结合模糊逻辑，开发了一种新型混合FO控制器。通过分数Lyapunov理论推导的算法保证了整个系统的稳定性，并且保证了同步误差向较小残差集的收敛。仿真表明，不仅在响应速度方面，而且在减少抖动现象方面，所提出的控制算法在安全通信中的能力。