Optimal Actuator Location of the Minimum Norm Controls for Stochastic Heat Equations
Optimization and Control
2023-03-31 v1
Abstract
In this paper, we study the approximate controllability for the stochastic heat equation over measurable sets, and the optimal actuator location of the minimum norm controls. We formulate a relaxed optimization problem for both actuator location and its corresponding minimum norm control into a two-person zero sum game problem and develop a sufficient and necessary condition for the optimal solution via Nash equilibrium. At last, we prove that the relaxed optimal solution is an optimal actuator location for the classical problem.
Keywords
Cite
@article{arxiv.1710.06079,
title = {Optimal Actuator Location of the Minimum Norm Controls for Stochastic Heat Equations},
author = {Donghui Yang and Jie Zhong},
journal= {arXiv preprint arXiv:1710.06079},
year = {2023}
}