在逐点状态约束下一个四阶线性系统的时间最优控制

Time optimal control problem for a fourth-order linear system with pointwise state constraints

在逐点状态约束下,最优控制问题的求解是很困难的,已有的最大值原理和形态规划理论很难用来求解在逐点状态约束下最优控制问题.本文讨论逐点状态约束下一个四阶线性系统的时间最优控制问题.我们采用转换的方法给出了最优时间与最优控制的具体表达式.

In optimal control field, it is very difficult to find the optimal control for an optimal control problem with point-wise state constraints. There is no effective way to calculate the optimal control for this kind of problem. A timeoptimal control problem Ph for a forth-order linear system with point-wise state constraints and terminal constraints is considered in this paper. By transforming problem Ph into a time-fixed problem RT with the same point-wise constraints and fewer terminal constraints, the solvability of the problem Ph is proved to be equivalent to that of RT, the relations between the solutions of these two problems are also established. For the problem RT, its corresponding problem ^↑RT without the point-wise state constraints can be solved easily. From the solution of ^↑RT, the optimal control of problem ^↑RT is then constructed. According to the relation between the solutions of the problem Ph and RT, the optimal control of Ph is consequently obtained. The main results are the solvability of the problem Ph and its explicit expressions of the optimal time and the optimal control.