状态二次型线性最优控制

本文研究一类性能指标中没有能量项,且控制是受约束的线性二次型最优控制问题,证明了两个分别适用于状态矩阵为稳定阵和非稳定阵的定理。按照本文给出的结果,最优控制是开关型的,而且容易在实时控制中实现。

Linear Optimal Control of State Quadratic Form

A kind of linear quadratic optimal control problem is investigated, in which the performance index does not include quadratic control term and the control is constrained. The system and performance index are represented respectively as follows:Two theorems have bsen proved:Theorem 1: If A is a stable matrix and under certain conditions, he optimal control is u = - sign{BTPX}, then the system will be closed-loop asymptotically stable; Theorem 2: If A is an unstable matrix and under certain conditions, the optimal con-trol isthen the system will also be closed-loop asymptotically stable.According to the results given, it can be concluded that the optimal control of this kind of problem is Bang-Bang control and can be realized easily in real time control.