基于投影法的不确定分数阶混沌系统自适应同步

针对一类具有未知参数、未知非线性函数及外部扰动的分数阶混沌系统，基于分数阶系统稳定性理论和Lyapunov稳定性理论，该文提出一种基于滑模自适应和投影法的同步控制策略。首先选取一类稳定的分数阶积分滑模面，运用自适应技术对不确定项进行估计，设计了同步控制器。然后对自适应设计中容易出现的增长型自适应律运用投影法进行修正，以保证参数有界，从而也保证控制输入有界。最后数值仿真证明了所设计控制器的正确性和有效性。

Adaptive Synchronization of Uncertain Fractional-order Chaotic Systems Based on Projective Method

Based on the stability theory of fractional-order system and Lyapunov stability theory, and using the sliding mode adaptive control and projective method, a synchronization control strategy is proposed for a class of fractional-order chaotic systems with uncertain parameters, uncertain nonlinear functions and external disturbances. A stable fractional-order integral sliding surface is selected and the adaptive laws are designed to estimate the uncertainties, consequently, the synchronization controller is obtained. Then, the projective method is introduced to modify above basic adaptive laws to prevent the adaptive parameters from diverging to infinite, thus, the boundedness of the control inputs is guaranteed. Finally, the numerical simulation result is presented to show the effectiveness and applicability of the proposed control strategy.