一种新型不确定分数阶混沌系统滑模同步控制方式

针对一类存在参数摄动、未知函数及外部扰动等不确定因素的分数阶混沌系统的同步控制问题，设计了一类具有新颖的分数型积分滑模面的同步控制器。所设计的新型分数阶滑模面抖震更小、收敛速率更快。提出了一种改进的分数阶非增长型自适应律，有效避免了随时间增长可能引起的控制量无界的问题。引入频率分布模型分析系统模型，并基于Lyapunov稳定性定理证明同步误差收敛，避免了直接用伪状态变量对同步误差系统进行分析的错误，形成了分数阶运算和整数阶同步控制方法有机结合的新方法。仿真结果证明了该方法的有效性。

A Novel Sliding Mode Synchronization Method of Uncertain Fractional-Order Chaotic Systems

A novel adaptive sliding mode synchronization controller for uncertain fractional order chaotic systems is proposed in this paper. The proposed controller can realize the synchronization of systems with parameters perturbation, function uncertainties, and exterior disturbance. The new sliding mode surface with fractional order has advantages of week chattering and high convergent rate. A novel fractional order adaptive updating law is proposed to prevent the estimations from increasing infinitely. The sliding mode surface and the parameter estimation error of the controller are modelled by utilizing frequency distribution model, and the convergence of the error system is verified by Lyapunov functions, avoiding the mistake caused by directly applying pseudo state variables for the analysis of system synchronization error. Simulation results demonstrate the effectiveness of the proposed scheme.