不确定离散系统的最优保性能控制

Optimal Guaranteed Cost Control for Uncertain Discrete Time Linear Systems

对一类具有范数有界时变参数不确定性的离散时间线性系统和一个二次型性能指标，研究其最优保性能状态反馈控制律的设计问题．通过采用线性矩阵不等式方法，导出了存在保性能控制律的一个充分必要条件，进而，证明了该条件等价于一个线性矩阵不等式的可解性问题，并用这组线性矩阵不等式的可行解给出了保性能控制律的一个参数化表示．在此基础上，通过建立并求解一个凸优化问题，给出了最优保性能控制律的设计方法．

For a class of discrete time linear systems with norm bounded time varying parameter uncertainty and a quadratic cost index, the problem of designing an optimal guaranteed cost state feedback controller is considered in this paper. A necessary and sufficient condition for the existence of guaranteed cost controllers is derived. Furthermore, it is shown that this condition is equivalent to the solvability problem of a system of linear matrix inequalities, and its solutions provide a parametrized representation of guaranteed cost controllers. Based on that, the design problem of the optimal guaranteed cost controller is formulated as a convex optimization problem, which can be solved by the existing convex optimization techniques. Finally, an example is given to illustrate the proposed results.