基于自适应模糊控制的分数阶混沌系统同步

摘要

本文主要研究了带有未知外界扰动的分数阶混沌系统的同步问题.基于分数阶Lyapunov稳定性理论，构造了分数阶的参数自适应规则以及模糊自适应同步控制器.在稳定性分析中主要使用了平方Lyapunov函数.该控制方法可以实现两分数阶混沌系统的同步，使得同步误差渐近趋于0.最后，数值仿真结果验证了本文方法的有效性.%In this paper the synchronization problem for fractional-order chaotic system with unknown external disturbance is investigated by adaptive fuzzy control. Based on the fractional Lyapunov stability theorem, an adaptive fuzzy controller, which is accompanied with fractional adaptation law, is established. Fuzzy logic system is used to approximate an unknown nonlinear function. The fuzzy approximation error can be canceled by the proposed fractional adaptation law. Just like the stability analysis in an integer-order chaotic system, the quadratic Lyapunov function is used to analyze the stability of the fractional-order closed-loop system. The control method can realize good synchronization performances between two fractional-order chaotic systems, and the synchronization error tends to zero asymptotically. Besides, the proposed controller can also guarantee the boundedness of all signals in the closed-loop system. Finally, the numerical simulation results illustrate the effectiveness of the proposed control method for fractional-order chaotic system in the presence of the external disturbances.