无穷时域上常微分方程的最优控制问题

数学物理学报 ›› 2026, Vol. 46 ›› Issue (5): 1884-1899.

无穷时域上常微分方程的最优控制问题

余行阳()

武汉大学数学与统计学院武汉 430072

收稿日期:2025-04-21 修回日期:2026-01-23 出版日期:2026-10-26 发布日期:2026-09-07
作者简介:余行阳, E-mail: 2556307949@qq.com

Infinite Horizon Optimal Control Problem for Ordinary Differential Equations

Xingyang Yu()

school of mathematics and statistics, Wuhan University, Wuhan 430072

Received:2025-04-21 Revised:2026-01-23 Online:2026-10-26 Published:2026-09-07

摘要/Abstract

摘要：

该文研究无穷时域上一类线性常微分方程的控制问题. 这类问题的特点是对于某些特定的控制, 微分方程的解可能会在有限时间上爆破, 这与过去研究的无穷时域上的最优控制问题都不同. 该研究目的是使用一种新方法来建立该问题的庞特里雅金最大值原理.

关键词: 最优控制, 常微分方程, 庞特里雅金最大值原理

Abstract:

This paper studies an infinite horizon optimal control problem governed by a kind of controlled linear ordinary differential equations. Corresponding to certain controls, the solutions of the equation may blow up at a finite time. It differs from the most infinite horizon optimal control problems in past publications. The purpose of this study is to develop a new method to establish Pontryagin Maximum Principle of optimal controls for such problem.

Key words: optimal control, ordinary differential equations, Pontryagin Maximum Principle

中图分类号:

O231.2

余行阳. 无穷时域上常微分方程的最优控制问题[J]. 数学物理学报, 2026, 46(5): 1884-1899.

Xingyang Yu. Infinite Horizon Optimal Control Problem for Ordinary Differential Equations[J]. Acta mathematica scientia,Series A, 2026, 46(5): 1884-1899.

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