Homogenization of some low-cost control problems

TL;DR

This paper investigates the asymptotic behavior of low-cost control problems, establishing new bounds and convergence results, including Gamma-convergence, for problems with weak data and measures, advancing the theoretical understanding of homogenization in control systems.

Contribution

It introduces new homogenization results for low-cost control problems with weakly converging data and measures, including improved bounds and Gamma-convergence analysis.

Findings

Established an improved lower bound for energy functionals with weak data.

Proved Gamma-convergence of a low-cost control problem with Dirichlet-type integrals.

Analyzed the asymptotic behavior of controls converging to measures.

Abstract

The aim of this article is to study the asymptotic behaviour of some low-cost control problems. These problems motivate the study of H-convergence with weakly convergingdata. An improved lower bound for the limit of energy functionals correspondingto weak data is established, in the periodic case. This fact is used to prove the Gamma-convergence of a low-cost problem with Dirichlet-type integral. Finally, we study the asymptotic behaviour of a low-cost problem with controls converging to measures.