反馈控制系统多性能约束指标的相容性

Consistency of multiple performance indices of feedback control systems

对一类线性随机系统的状态反馈控制,研究极点配置指标、被控输出对范数有界外扰的H_∞抑制指标及稳态状态方差上界指标的相容性,希望为实际控制系统多性能指标的选定提供理论依据,用线性矩阵不等式(LMI)方法分别刻画了极点指标约束下H_∞指标的取值范围、以及相容极点指标和H_∞指标约束下稳态方差上界指标的取值范围,对上述三类相容指标约束的控制问题给出求取满意控制策略的有效方法。文中结论用数值算例作了说明。

Consistency of performance indices is studied for a class of linear stochastic systems via state feedback control. These constraints consist of pole assignment index, H∞ rejection index from norm-bounded exogenous disturbance to the controlled output and upper bound on steady state variance. The study aims to provide a theoretical basis for the choice of desired multi-performance indices on some practical control systems. Based on linear matrix inequality (LMI) approach, the region of H∞ index which is consistent to the given pole index, and a good region of upper state-variance index which is consistent to the given consistent pole and H∞ index are presented respectively. Furthermore, a method to find a satisfactory control strategy is provided for the considered systems under the above three consistent constraints. Finally, the results concerned is illustrated by a numerical example.