全空间中带位势热方程的采样时间最优控制

数学物理学报 ›› 2023, Vol. 43 ›› Issue (4): 1269-1283.

全空间中带位势热方程的采样时间最优控制

卢维平(),刘汉兵^*()

中国地质大学(武汉)数学与物理学院武汉 430074

收稿日期:2022-05-12 修回日期:2023-03-06 出版日期:2023-08-26 发布日期:2023-07-03
通讯作者: 刘汉兵 E-mail:18640459289@163.com;hanbing272003@aliyun.com
作者简介:卢维平，E-mail: 18640459289@163.com
基金资助:
中央高校基本科研业务费, 中国地质大学(武汉)(CUGSX01)

Sampled-Data Time Optimal Control for Heat Equation with Potential in $\mathbb{R} ^{n}$

Lu Weiping(),Liu Hanbing^*()

School of Mathematics and Physics, China University of Geosciences, Wuhan 430074

Received:2022-05-12 Revised:2023-03-06 Online:2023-08-26 Published:2023-07-03
Contact: Hanbing Liu E-mail:18640459289@163.com;hanbing272003@aliyun.com
Supported by:
Fundamental Research Funds for the Central Universities, China University of Geosciences, Wuhan(CUGSX01)

摘要/Abstract

摘要：

该文考虑全空间中带常值位势的热方程的采样时间最优控制问题, 给出了一定条件下时间最优控制的存在性和最小范数时间最优控制满足的Pontryagin 最大值原理. 为得到时间最优控制的存在性, 该文建立了新的能观不等式, 通过该不等式得到控制系统的采样渐近零能控, 并结合Fenchel对偶理论对实现渐近零能控的控制的最小代价进行了刻画.

关键词: 时间最优控制, 采样控制, 渐近零能控, Pontryagin最大值原理

Abstract:

In this paper, the sampled-data time optimal control problem of heat equation with constant potential in whole space is considered. We establish the existence of time optimal control under certain conditions and the Pontryagin's maximum principle that time optimal control with minimal norm satisfies. In order to obtain the existence of time optimal control, a new observability inequality is established. The null approximate controllability of the sampled-data control system is obtained by using the observability inequality, and the minimum cost to achieve the null approximate controllability is characterized by Fenchel duality theory.

Key words: Time optimal control, Sampled-data control, Null approximate controllability, Pontryagin's maximum principle

中图分类号:

O232

卢维平,刘汉兵. 全空间中带位势热方程的采样时间最优控制[J]. 数学物理学报, 2023, 43(4): 1269-1283.

Lu Weiping,Liu Hanbing. Sampled-Data Time Optimal Control for Heat Equation with Potential in $\mathbb{R} ^{n}$[J]. Acta mathematica scientia,Series A, 2023, 43(4): 1269-1283.

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