一类线性常微分方程的时间最优控制问题

Time Optimal Control Problem for a Class of Ordinary Differential Equations

在Rn空间中研究一类线性常微分方程的时间最优控制问题,证明了与控制量大小有关的最优时间函数是连续的且单调递减的,在此基础上建立一类范数最优控制问题和时间最优控制问题的等价性,此控制系统的目标集是包含原点的闭球.

The time optimal control problem of a class of linear ordinary differential equation in Rn space is considered.The minimal time function dependened on the size of control is proved to be continuous and strictly monotonically decreasing.Based on this,the equivalence between norm optimal control problem and time optimal control problem is obtained.The target set of the control system is a closed sphere containing the origin.