新分数阶混沌系统的电路仿真及自适应滑模控制

Circuit Simulation and Adaptive Sliding Mode Control of New Fractional Order Chaotic Systems

根据典型的整数阶Liu混沌系统提出一个同一未知参数控制的新分数阶混沌系统,通过对新分数阶混沌系统进行平衡点、初始值的敏感性、相轨迹图、李雅普诺夫指数图以及分岔图的研究,新分数阶混沌系统的混沌特性得到了充分的验证;使用Multisim对系统进行电路仿真实现,实验结果验证了系统进行电路实现的可行性;最后设计自适应滑模控制器,得到系统在具有扰动干扰以及未知参数影响下的系统同步.

According to the typical integer order Liu chaotic system,a new fractional order chaotic system controlled by the same unknown parameter is proposed.The chaotic characteristics of the new fractional order chaotic system are fully verified by studying the equilibrium point,sensitivity of initial value,phase trajectory diagram,Lyapunov exponent diagram and bifurcation diagram of the new fractional order chaotic system;The circuit simulation of the system is realized by Multisim,and the experimental results verify the feasibility of the circuit implementation of the system;Finally,an adaptive sliding mode controller is designed to obtain the system synchronization under the influence of disturbance and unknown parameters.