一类受扰不确定混沌系统的最优控制

Optimal Control of a Class of Uncertain Chaotic System with External Disturbances

基于状态反馈精确线性化,研究了具有外界扰动作用下的不确定混沌系统的线性二次型最优控制器设计问题。首先通过微分同胚坐标变换将受扰动混沌系统模型转变为无扰动的伪线性系统模型;然后给出基于二次型性能指标的最优控制器设计方法。与现有方法相比,文中线性二次型问题的最优解不仅可以写成统一的解析表达式而且实现了求解过程的规范化,线性状态反馈控制律简单且便于工程实现,因而广泛应用于实际工程问题中。最后对Liu混沌系统进行仿真,仿真结果证明了该方法的有效性。

Based on state feedback exact linearization,the linear quadratic optimal control problem for uncertain chaotic systems with external disturbances is researched.Firstly,the perturbed chaotic system model into undisturbed pseudo linear system model by the differential homeomorphism is transfomed.Then the optimal controller design method based on quadratic performance index is given.Compared with the existing method,the optimal solution of linear quadratic problem not only can be written as a unified analytical expressions,but also realize the standardization of solving process.Linear state feedback control law is simple and easy for engineering realization.At last,the simulation of Liu chaotic system results shows the effectiveness of the method.