反步自适应方法实现混沌系统的同步

Adaptive Backstepping Synchronization of Chaotic Systems

针对基于滞环非线性参数未知的多涡卷混沌系统,提出了一种自适应反步变结构的控制方案来实现其同步。通过逐步修正的方法设计镇定控制器,在每一步把状态坐标的变化、不确定参数的调节函数和一个Lyapunov函数的虚拟系统的镇定函数联系起来,以达到实现系统的全局调节。采用所设计的控制器实现了两个混沌系统的同步控制,使得误差系统在有限时间内到达所设定的滑模面,并沿着滑模面渐进收敛到原点,同时估计出系统中存在的未知参数。由于自适应算法和滑模方法的使用,控制器对参数扰动和外部干扰具有较强的抑制作用,理论分析和仿真结果验证了所提出方法的有效性。

In this paper, a synchronization method of adaptive backstepping sliding - mode control is presented based on the multi - scroll chaotic systems with hysteresis nonlinear function and unknown parameters. The strategy is designed by a step -by- step procedure interlacing, at each step, a coordinate transformation and the design of a virtual control via a Lyapunov technique, and the definition of a tuning function are derivated, then, the globally control of the system is obtained. Finally, synchronization is achieved used the controller. The error system arrives at the sliding - mode in finite time, and then the error system is asymptotically stable in the origin. At the same time, the identification of the unknown parameters is obtained. Because of using the adaptive arithmetic and sliding - mode control, the control is robust for parameter uncertainties and disturbances. The analysis and simulation results prove the effectiveness and feasibility of the method.