On the switching behavior of sparse optimal controls for the one-dimensional heat equation

2017/05/09 by Fredi Troeltzsch, Troeltzsch, Fredi, Daniel Wachsmuth +1 · 1 citation
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #math.OC

paper · pdf · doi:10.48550/arxiv.1705.03191

arxiv created 2017/05/10 · arxiv updated 2017/05/11

Abstract

An optimal boundary control problem for the one-dimensional heat equation is considered. The objective functional includes a standard quadratic terminal observation, a Tikhonov regularization term with regularization parameter ν, and the L¹-norm of the control that accounts for sparsity. The switching structure of the optimal control is discussed for ν≥ 0. Under natural assumptions, it is shown that the set of switching points of the optimal control is countable with the final time as only possible accumulation point. The convergence of switching points is investigated for ν\searrow 0.

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