一类奇异时滞系统的奇异二次指标最优控制问题

Singular LQ problem for a class of singular system with time delay

利用基本的代数等价变换 ,将一类奇异滞后系统的奇异二次指标最优控制问题转化为正常状态滞后系统的非奇异二次指标最优控制问题 ,并讨论了二者的等价性。在一些常规条件下 ,给出了问题的解 ,并把最优控制综合为最优状态反馈。

Using elementary linear algebra and the equivalence principle, singular LQ problem for a class of singular systems with time delay is discussed and the relationship between the problem and the singular or nonsingular LQ problem for standard systems with delayed state is obtained. Under some general conditions, the optimal control and the optimal state of the LQ problem are given. The optimal control can be synthesized as state feedback.