混沌系统不稳定平衡点的镇定及其在蔡氏电路中的应用(英文)

Stabilization of unstable equilibria of chaotic systems and its applications to Chua's circuit

基于混沌系统的遍历性和状态PI调节器理论 ,提出一类混沌系统不稳定平衡点的镇定和设定点跟踪新方法 ,给出用于控制器参数设计的Lyapunov矩阵不等式 .对于分段线性混沌系统 ,如蔡氏电路 ,可通过控制理论中的极点配置技术来设计控制器参数 .该方法对系统参数变化具有很强的鲁棒性 ,能够消除外部定值扰动 .将该方法用于蔡氏混沌电路不稳定平衡点的镇定 ,取得了满意的结果 .

Based on the ergodicity of chaos and the state PI regulator approach, a new method was proposed for stabilizing unstable equilibria and for tracking set-point targets for a class of chaotic systems with nonlinearities satisfying a specific condition. A criterion was derived for designing the controller gains, in which control parameters could be selected by solving a Lyapunov matrix inequality. In particular, for piecewise linear chaotic systems, such as Chua's circuit, the control parameters can be selected via the pole placement technique in linear control theory. More importantly, this method has high robustness to system parametric variations and strong rejection to external constant-disturbances. For verification and demonstration, the design method is applied to the chaotic Chua's circuit, showing satisfactory simulation results.\;