分数阶Chen系统的控制与反相延迟同步

摘要

Fractional order chaotic system has a very great prospect in the fields of secure communication and oscillator design. In this article the local stability of the fractional order Chen chaotic system at various equilibrium points is analyzed using the stability theory of fractional order linear systems. Feedback control is designed to realize chaos control of the fractional order Chen system according to fractional order Routh-Hurwitz criterion, and provide the sufficient conditions suppressing chaos to a unstable equilibrium point. Combining inverse synchronization with lag synchronization, a novel fractional order inverse lag synchronization method is proposed. A corresponding nonlinear controller is designed to reach the inverse lag synchronization of fractional order Chen system. Numerical simulation shows effective and feasibility of the proposed method.%分数阶混沌系统在保密通信和振荡器设计等领域有着巨大的应用前景。利用分数阶线性系统的稳定性理论分析了分数阶Chen混沌系统在平衡点处的局部稳定性。设计线性反馈控制并依据分数阶Routh-Hurwitz准则实现了分数阶Chen系统的混沌控制，提供了抑制混沌到不稳定平衡点的充分条件。结合反相同步和延迟同步，提出了分数阶系统的反相延迟同步，并设计相应的非线性控制器实现了分数阶Chen系统的反相延迟同步。数值仿真结果表明了该方法的有效性和可行性。