加速反馈和延迟反馈控制一个新的混沌系统

针对一个新的混沌系统,研究了其混沌控制问题。首先,设计了一个加速反馈控制器将系统稳定到失稳的平衡点,并用Routh-Hurwitz判据对受控系统进行了稳定性分析,分析结果表明,受控系统可以稳定到非零平衡点,但不能稳定到零平衡点,并与状态变量反馈控制方法相比较显示了其优越性;其次,应用泰勒展开定理,设计了一种近似的延迟反馈控制方法,将受控的系统稳定到希望的周期轨道上或平衡点;最后通过数值仿真证明了这两种方法具有快速的稳定效果。

Speed feedback and delayed feedback control of a new chaotic system

The problem of chaos control for a new chaotic system is studied primarily. Firstly,the chaotic system is brought to its unstable equilibrium points by designing a speed feedback controller. The Routh-Hurwitz criterion is used to analyze the stability of the controlled system, and the result indicates that the controlled system can converge to nonzero equilibrium points, but it cannot converge to zero equilibrium point.A comparison is made between the speed feedback control method and the method of state-variable-feedback control to show the superiority of the presented method. Secondly,an approximate delayed feedback control method is designed by applying Taylor theorem,and the controlled system is stabilized in the expected periodic orbits or at equilibrium points. The fast stabilization effect of these two kinds of control methods are proved by numerical simulation.