类Chen-Qi混沌系统的固定时间自适应同步控制

Fixed-Time Adaptive Synchronization Control of Chen-Qi-like Chaotic System

类Chen-Qi四维混沌系统的渐近稳定控制的同步误差不能在有限时间内收敛到零,有限时间控制的同步误差收敛到零的状况与初值有关.因此,本文应用固定时间控制技术,设计了自适应控制器和参数估计律,试图使得驱动系统与同类型的参数未知的响应系统在固定时间内达到同步,完成了理论证明.应用数值仿真考察同步误差收敛到零的状况.选取不同参数值,不同状态初值,考察状态时程图、同步误差曲线等.结果表明:混沌运动时,固定时间内同步误差收敛到零的效果较好,与状态初值无关,收敛时间符合理论计算值;周期运动时,固定时间内前三个状态的同步误差收敛到零的效果较好,收敛时间符合理论计算值,但第四个状态的同步误差的收敛时间不符合理论计算值,其原因是系统存在的三次非线性项的不平衡、不匹配.

For Chen-Qi-like four-dimensional chaotic system,controllers designed with Lyapunov stability theory make synchronization errors converge to zero asymptotically.Finite-time control technique improve it,but the errors are various with initial conditions.Therefore,fixed-time control technique is applied to design an adaptive controller and parameter estimation law,try to make the drive system synchronizing with a same type response system of unknown parameters in a fixed time.which is proven theoretically.State time history diagrams and synchronization error curves are investigated by numerical simulation with various parameters and initial state values.The results show that:during chaotic motion,the effects of synchronization errors converge to zero within a fixed time is only related to system parameters,not dependent of the initial state value,and the convergence time conforms to the theoretical calculation;during periodic motion,the effects of first three synchronization errors converge to zero within a fixed time is good,their convergence time conforms to the theoretical calculation.However,the convergence time of the last synchronization error does not conform to the theoretical calculation,due to the imbalance and mismatch of the cubic nonlinear term in the system.