Relaxation of optimal control problems driven by nonlinear evolution equations
type: Item
instance of: scholarly article
title: Relaxation of optimal control problems driven by nonlinear evolution equations
zbMATH Open document ID: 1458.49014
author: Leszek Gasiński
author: Nikolaos S. Papageorgiou
published in: Evolution Equations and Control Theory
publication date: 2021-01-13T00:00:00Z
review text: The paper concerns the analysis of an optimal control problem driven by a nonlinear evolutionary ODE. Specifically, the problem is to minimize an integral functional of two variables \(x,u\) depending on time \(t\). The function \(x\) solves a nonlinear differential equation with coefficients depending on the function \(u\). In its turn, \(u(t)\) belongs to a multifunction \(U(t,x(t))\). Since the problem is not convex, optimal pairs need not exist. A classical strategy is then to relax the problem, i.e., to enlarge the system in such a way that any minimizing sequence has a limit. Without resorting to Young measures, the authors relax the problem by introducing the convexifications of the cost and of the multifunction \(U\). The solutions of the convexified problems converge in suitable topologies; moreover also the corresponding cost functions converge.
reviewed by: Giuliano Lazzaroni
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 7293860
zbMATH Keywords: evolution triple
zbMATH Keywords: admissible relaxation
zbMATH Keywords: weak norm
zbMATH Keywords: optimal pair
zbMATH Keywords: cost functional
MaRDI profile type: Publication
full work available at URL: eect.2020050
OpenAlex ID: W3013358803
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DOI: 10.3934/EECT.2020050
description: scientific article; zbMATH DE number 7293860