一类不确定分数阶混沌系统的滑模自适应同步

基于滑模自适应控制理论、Lyapunov稳定性理论和分数阶线性系统稳定性理论，在考虑系统存在模型不确定和外部扰动的情况下，选用一种具有较强鲁棒性的分数阶滑模曲面，设计了合适的自适应滑模控制器。所设计的控制器能够将系统状态控制到滑模面上，实现两个不确定分数阶混沌系统的同步，且不需事先知道不确定项上界。该控制器结构简单，控制代价小，具有较好的通用性，对未知扰动具有较强的鲁棒性。数值仿真验证了该方法的正确性和有效性。

Sliding mode adaptive synchronization for a class of fractional-order chaotic systems with uncertainties

A fractional-order sliding mode adaptive control approach was introduced to synchronize chaos of a class of fractional-order chaotic systems with uncertainties. The effects of model uncertainties and external disturbances were fully taken into account. An appropriate robust fractional sliding mode adaptive controller was designed by adopting a fractional sliding surface with strong robustness, and using sliding mode adaptive control theory, Lyapunov stability theory and fractional-order linear systems stability theory. The control law can ensure the occurrence of the sliding motion, and achieve synchronization between the drive system and response system. The upper bound of uncertainties was not needed in the proposed controller. The designed controller is not complicated mathematically and easy to implement. The fractional adaptive sliding mode control approach can be applied to control a broad range of nonlinear fractional-order chaotic systems with uncertainties. Numerical simulation was presented to show the efficiency and applicability of the proposed control strategy.