具有未知参数的混沌系统的有限时间滑模同步控制

针对带有未知参数和非线性输入的两个不同的混沌系统之间的同步问题进行研究. 提出一个相比于传统滑模面具有更快收敛速度的终端滑模面, 并结合自适应控制理论和滑模控制理论, 设计一个自适应滑模控制律, 使同步误差在有限时间内收敛到滑模面, 并沿滑模面在有限时间内收敛到零点, 最终实现两个不同的混沌系统之间的同步. 最后, 以带有不确定性和外部扰动的Lorenz 系统和Liu 系统为例进行数值仿真, 仿真结果表明, 同步误差在有限时间内收敛到零点, 从而验证了所设计控制律的有效性和可行性.

Finite-time sliding mode synchronization control of chaotic systems with uncertain parameters

The problem of chaos synchronization between two different chaotic systems with uncertain parameters and nonlinear inputs is investigated. A terminal sliding surface with a faster convergence speed than conventional sliding surface is introduced. Based on the adaptive control theory and the sliding mode control technique, an adaptive sliding mode controller is designed to guarantee the convergence of synchronization errors to the sliding surface and zero equilibrium in finite-time. Finally, numerical simulations about the Lorenz system and the Liu system are carried out, and simulation results show that synchronization errors converge to zero in finite-time, and the effectiveness and applicability of the proposed control scheme is proved adequately.