具有无限类混沌吸引子的保守混沌系统自适应滑模控制

Self-adaptive sliding mode control for conservative chaotic systems with infinite chaos-like attractors

提出一个具有类混沌吸引子的三维保守混沌系统,新系统在Sprott A基础上增加了一个余弦项并将常数项改为变参项。首先,分析了该系统的典型混沌特性,着重分析了参数变化时的李雅普诺夫指数、时序图以及相应相图。然后,通过改变初始值,得到获得无限类共存吸引子的方法并进行仿真验证。最后,在不确定和干扰作用下设计自适应滑模控制器,实现对新混沌系统的同步控制,并利用Matlab仿真验证所提控制器的有效性。

A three-dimensional conservative chaotic system with chaos-like attractors was proposed in this paper.The new system was constituted on the basis of Sprott A by adding a cosine term and changing the constant term into the variable term.The typical chaotic characteristics of the system were then analyzed with the emphasis on the Lyapunov exponents,the sequence diagram and the corresponding phase diagram of the system with parameter variation.By changing the initial value,the method of obtaining infinite class coexisting attractors was obtained and further verified by simulation.Finally,a self-adaptive sliding mode synchronization controller was designed to realize the synchronization control of the new chaotic system under the uncertainties and disturbances.The effectiveness of the proposed controller was verified by Matlab simulation.