分数阶混沌系统的主动滑模同步

摘要

This paper proposed an active sliding mode method,which combines the active control theory and the sliding mode theory to synchronize fractional-order chaotic systems.In the active sliding mode control strategy, first the fractional-order integrator was introduced to obtain a novel sliding surface containing all the state compo-nents in the system,and the fractional order chaotic system is stable in the sliding surface.Then the gain matrix of the active sliding mode controller was obtained using the pole placement method.The existence and the stabili-ty of the proposed controller were analyzed based on Lyapunov stability theory and fractional stability theory.The simulation results of the fractional order Lorenz system verify the effectiveness of the proposed method.%结合主动控制和滑模控制原理，提出了一个同步分数阶混沌系统的主动滑模控制方法。该方法首先用分数阶积分对所有维状态分量设计一个滑模面，分数阶混沌系统在该滑模面上稳定。然后采用极点配置的方法获得主动滑模控制器中的增益矩阵。应用 Lyapunov 稳定性理论、分数阶系统稳定理论对所提的控制器的存在性和稳定性分别进行了分析。对分数阶Lorenz 系统进行数值仿真，仿真结果验证了该方法的有效性。