Advantages for controls imposed in a proper subset
Gengsheng Wang, Yashan Xu

TL;DR
This paper investigates time optimal control problems for heat equations, demonstrating that controls on proper subsets of the domain exhibit existence and bang-bang properties, unlike controls on the entire domain, and reveals a new eigenfunction property.
Contribution
It establishes the conditions under which existence and bang-bang properties hold for controls on subsets, and introduces a novel eigenfunction property for the Laplacian.
Findings
Existence of time optimal controls on proper subsets
Bang-bang property holds on proper subsets
A new eigenfunction property for the Laplacian
Abstract
In this paper, we study time optimal control problems for heat equations on . Two properties under consideration are the existence and the bang-bang properties of time optimal controls. It is proved that those two properties hold when controls are imposed on some proper subsets of ; while they do not stand when controls are active on the whole . Besides, a new property for eigenfunctions of with Dirichlet boundary condition is revealed.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems
