具有控制约束的分数阶混沌系统柔性同步控制

Adaptive soft variable structure controller with control constraints for synchronization of fractional-order chaotic systems

研究具有控制约束的两个相同分数阶混沌系统的同步问题.首先,在不消除非线性项的情况下,基于比例控制与自适应控制理论,设计线性自适应切换控制器,实现分数阶混沌系统的同步;其次,考虑到控制器存在约束,利用能够提供无限子控制器的柔性变结构控制策略对线性控制器进行改进,设计柔性变结构控制器,以应对控制的约束,并对线性控制器进行优化;同时,基于分数阶系统Mittag-Leffler稳定判定定理对误差系统的稳定性进行证明.在兼顾系统稳定性与鲁棒性的情况下,可以缩短系统的调整时间,并有效抑制抖振.最后,利用所设计的自适应柔性控制器实现分数阶Chen系统的混沌同步,并通过仿真对比两控制器控制效果,从而验证柔性变结构方法在具有约束的分数阶混沌系统同步控制中的优越性.

The synchronization of two same fractional-order chaotic systems with control constrain is investigated.Firstly,based on the linear control theory and adaptive control theory,an adaptive proportional switching control scheme is designed without eliminating the nonlinear part.Then,considering the constraints of the controller,the linear part of the controller is improved using the soft variable structure method which can provide infinite sub-controllers.The soft variable controller is designed for dealing with the control constrain and optimizing the linear controller.At the same time,the stability of the error systems is proved based on the fractional-order Mittag-Leffler theory.Giving consideration to the stability and the robustness of the system,the adjustment time is shortened and the chattering is effectively suppressed.Finally,by using the designed controller,the synchronization of the fractional-order Chen chaotic system is realized.The numerical simulation results show the effectiveness and feasibility of the designed controller.The advantages of the soft variable structure method,which is used in the control of synchronization of fractional-order chaotic systems with control constrain,are verified by comparing the simulation of the two controllers.