一种四维混沌系统的逆最优控制

Inverse Optimal Control for a Four-Dimensional Chaotic System

采用逆最优控制方法为一种四维混沌系统设计了一个线性状态反馈控制器.基于Lyapunov稳定性理论,证明了所设计的控制器能够使受控系统全局渐近稳定到系统的零平衡点,并且使所提出的目标泛函取得极小值.两组数值仿真均表明,所设计的控制器是实用有效,易于实现,并且具有很好的鲁棒性.在不同的初始条件下,所设计的控制器可以将受控四维混沌系统的混沌轨道很快控制到系统的零平衡点.

A linear state feedback controller is designed for controlling a four-dimensional chaotic system by the inverse optimal controlling approach. Based on the Lyapunov stability theory, the designed controller is proved enable to globally stabilize asymptotically the controlled system to return to its zero balance point and minimize the proposed cost functional. Two sets of data from numerical simulation show the effectiveness, readiness and robustness of the controller, The chaotic trajectory of the controlled 4-D system can be controlled to return to its zero balance point under different initial conditions.