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arXiv · 1710.06079

Optimal Actuator Location of the Minimum Norm Controls for Stochastic Heat Equations

Donghui Yang·Jie Zhong
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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.

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Donghui Yang, Jie Zhong. 2017-10-17. Optimal Actuator Location of the Minimum Norm Controls for Stochastic Heat Equations. https://doi.org/10.3934/mcrf.2018046

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