超混沌系统的多变量驱动误差反馈控制同步方法

Synchronization control method of hyperchaotic systems by multi-variables driving and error feedback

基于Lyapunov稳定性理论,提出实现连续时间超混沌系统同步的多变量驱动误差反馈控制同步定理,确定了控制参数的范围。同步系统的反馈控制器由线性反馈和非线性反馈2部分组成,并受驱动系统的所有变量驱动。提出采用同步稳定性、同步鲁棒性、同步稳态误差、同步精度、同步建立时间、同步化区域和同步动态特性等描述混沌同步系统性能的7项指标,获得控制参数影响同步系统性能的机理,即控制参数通过改变系统的条件Lya-punov指数而影响系统的同步性能。对Rssler超混沌系统的数值仿真研究表明:多变量驱动误差反馈同步方法具有不需要分解系统、不需要计算响应系统的条件Lyapunov指数和同步收敛快的特点。

Based on the Lyapunov stability theory, a new hyperchaotic synchronization method called multi-variables driving and error feedback control was presented, and the range of control parameters was determined. The feedback controller was composed of linear and nonlinear feedback, and driven by all variables of the driving system. To describe the performances of synchronization chaotic system, seven indexes including stability, robustness, stable state error, precision, setup time, range and dynamic characteristic were put forward. The relations between the performance index and the controller parameters are discussed. The numerical simulation results of Roessler hyperchaotic system show that this method has many merits such as no need of structure departing, calculation of the condition Lyapunov exponents and fast synchronization.