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Some numerical results for control of 3D heat equations using Nash equilibrium

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Abstract

This article deals with some numerical strategies to solve control problems for heat equations with Dirichlet boundary conditions. We assume that we can act on the system through two controls. We use a non-cooperative bi-objective optimization strategy, to which we define the associated Nash equilibrium. More precisely, for such problems, we look for Nash equilibrium associated with optimal cost functionalities, which correspond to appropriate non-cooperative strategies. To numerically calculate the solutions, we combine finite difference methods in time and finite element methods in space. In each system presented, we seek to solve the discretized problems using three iterative methods: Fixed Point, Gradient with Fixed Step, and Conjugated Gradient, and the developed algorithms will be analyzed and compared. The data programming and computational simulations are performed in the software FreeFem ++ and Matlab.

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  1. Coordenação de Matemática - Universidade Estadual do Piauí, Teresina, PI, Brazil

    Pitágoras Pinheiro de Carvalho

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  1. Pitágoras Pinheiro de Carvalho
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Correspondence to Pitágoras Pinheiro de Carvalho.

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Communicated by Luz de Teresa.

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de Carvalho, P.P. Some numerical results for control of 3D heat equations using Nash equilibrium. Comp. Appl. Math. 40, 92 (2021). https://doi.org/10.1007/s40314-021-01488-5

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  • DOI: https://doi.org/10.1007/s40314-021-01488-5

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