不确定离散广义线性系统的保性能最优控制

Optimal guaranteed cost control for uncertain discrete-time singular linear systems

对一类具有范数有界时不变参数不确定性的广义离散时间线性系统和一个二次型性能指标,研究了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条件,进而证明了该条件可化为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,最后用例子说明了该方法的应用。

For a class of discrete-time singular linear systems with norm-bounded time-unvarying parameter uncertainty and a quadratic cost index, the problem of designing an optimal guaranteed performance state feedback controller is considered. A sufficient condition for the existence of guaranteed cost controllers is derived. Furthermore, it is shown that this condition is a solvable problem of a system of linear matrix inequalities (LMI), and its solutions provide a parameterized representation of guaranteed cost controllers. Based on this, 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.