Minimal Time Impulse Control of an Evolution Equation
Minimal Time Impulse Control of an Evolution Equation
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DOI：
10.1007/s10957-019-01552-5
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发表时间：
2019-07
影响因子：
1.9
通讯作者：
Yueliang Duan;Lijuan Wang;Can Zhang
中科院分区：
文献类型：
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作者：
Yueliang Duan;Lijuan Wang;Can Zhang
研究了一类具有脉冲控制的线性发展方程的最小时间控制问题。每个问题取决于两个参数：控制约束的上界和脉冲时间的时刻。这样一个问题的目的是找到一个最佳的脉冲控制（在一定的控制约束集），它引导的解决方案的发展方程从一个给定的初始状态到一个给定的目标集尽可能快。本文研究了这类问题的最优控制的存在性，利用Hahn-Banach定理的几何形式，证明了最优控制的bang-bang性质，从而得到了最优控制的唯一性;我们还建立了该问题的最小时间函数关于上述两个参数的连续性，并讨论了当两个参数收敛时最优控制的收敛性。
This paper is concerned with a kind of minimal time control problem for a linear evolution equation with impulse controls. Each problem depends on two parameters: the upper bound of the control constraint and the moment of impulse time. The purpose of such a problem is to find an optimal impulse control (among certain control constraint set), which steers the solution of the evolution equation from a given initial state to a given target set as soon as possible. In this paper, we study the existence of optimal control for this problem; by the geometric version of the Hahn–Banach theorem, we show the bang–bang property of optimal control, which leads to the uniqueness of the optimal control; we also establish the continuity of the minimal time function of this problem with respect to the above mentioned two parameters, and discuss the convergence of the optimal control when the two parameters converge.