一类不确定分数阶混沌系统同步的自适应滑模控制方法

摘要

针对一类系统不确定及受外界干扰的分数阶混沌系统,本文首先将分数阶微积分应用到滑模控制中,构造了一个具有分数阶积分项的滑模面.针对系统不确定及外界干扰项,基于分数阶Lyapunov稳定性理论与自适应控制方法,设计了一种滑模控制器以及分数阶次的参数自适应律,实现了两不确定分数阶混沌系统的同步控制,并辨识出相应误差系统中不确定项及外界干扰项的边界.在分数阶系统稳定性分析中使用的分数阶Lyapunov稳定性理论及相关函数都可以很好地运用到其它分数阶系统同步控制方法中.最后数值仿真验证了所提控制方法的可行性与有效性.%For one class of fractional-order chaotic system with systematic uncertainties and external disturbances,firstly,fractional calculus is applied into sliding controller,and a sliding surface with a fractional integral term is designed.Based on the theory of fractional Lyapunov stability and adaptive control,a sliding mode controller with the fractional-order adaptive laws of the parameters is proposed to achieve the synchronization of two uncertain fractional-order chaotic systems emphasizing the systematic uncertainties and the external disturbances,and the bounds of uncertainty and the disturbance in corresponding error system are estimated.It should be pointed out that the fractional Lyapunov stability theorem and functions introduced in the stability analysis of the fractional-order chaotic systems can be applied to many other control methods for fractional-order nonlinear systems.Finally,numerical examples are given to verify the effectiveness and feasibility of the proposed control method.