参数未知多响应混沌系统的同步及参数估计

Synchronization and parameter estimation of multiple-response chaotic systems with unknown parameters

研究了一种单驱动多响应的不确定异构混沌系统的同步及参数估计问题。利用Lorenz系统同时驱动Yang系统和Liu系统(三个系统的参数均未知),构成一个单驱动多响应的不确定异构混沌系统。基于Lyapunov稳定性定理和自适应控制方法,给出自适应控制器的表达式和参数自适应率;引入尺度因子,研究了该单驱动多响应混沌系统两种不同形式的混合同步,并对未知参数进行估计,理论证明了该方法的可行性。仿真结果表明单驱动多响应的不确定异构混沌系统可以实现较好的同步,能准确地估计出系统中所有未知参数的值。

The synchronization and parameter estimation of an uncertain heterogeneous chaotic system with single-drive and multiple-response are investigated.By using Lorenz system to drive Yang system and Liu system simultaneously(parameters of the three systems are unknown),an uncertain heterogeneous chaotic system with single-drive and multiple-response is constructed.Based on Lyapunov stability theory and adaptive control method,the expression of adaptive controller and updating rule of parameters are given.Two different forms of mixed synchronization of the chaotic system with single-drive and multiple-response are investigated by,introducing the scaling factor,and the unknown parameters are estimated.The feasibity of the method is proved theoretically.The simulation results show that the uncertain heterogeneous chaotic system with single-drive and multiple-response can achieve better synchronization and accurately estimate the values of all unknown parameters in the system.