全空间中带位势热方程的采样时间最优控制

Abstract

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

CLC Number:

O232

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

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