不确定广义系统的弹性保性能控制

Resilient guaranteed cost control for uncertain descriptor systems

将弹性控制器的设计思想引入到一类不确定广义系统中,利用线性矩阵不等式(LMI)方法,研究被控对象与控制器同时存在摄动的弹性保性能控制问题。针对控制器存在加法式摄动情形,以线性矩阵不等式约束条件给出了广义系统弹性保性能的充要条件,并以线性矩阵不等式的可行解给出了相应的控制器设计方法,通过求解具有线性矩阵不等式约束的凸优化问题,给出了性能上界最小意义下弹性控制器的设计。数值仿真表明了该设计方法的可行性。

The designation idea of resilient controller is introduced to a class of uncertain descriptor system. Based on linear matrix inequality （LMI） techniques, the problem of guaranteed cost control is addresed, where the uncertainties exist both in the systematic matrix and in the controller gain. Under the additive perturbation, the sufficient and necessary condition of resilient guaranteed cost is presented, and the corresponding controller design is given in terms of the feasible solutions of LMIs. Through solving the convex optimization problem with LMI constraints, in the sense of minimizing cost upper bound, the design of resilient controller is given. A numerical example is Riven to illustrate the feasibility of the designed method.