Bi-objective and hierarchical control for the Burgers equation
type: Item
instance of: scholarly article
title: Bi-objective and hierarchical control for the Burgers equation
zbMATH Open document ID: 1542.93183
author: Fágner D. Araruna
author: Enrique Fernández-Cara
author: Luciano Cipriano da Silva
published in: Journal of Evolution Equations
publication date: 2024-07-10T00:00:00Z
review text: This paper considers some bi-objective and hierarchical control problems for the Burgers equation. More precisely, Burgers equation is controlled by three distributed controls, each of them being assigned to a different task. To the first control, called the leader, there are associated two other controls called the followers. The triplet formed by these controls solves an hierarchical Stackelberg-Nash control problem. The main contribution of this paper is the formulation and the solution of Nash and Stackelberg-Nash control problems in a non-linear setting. These results may be seen as a first step for similar control problem in more complex nonlinear situations such as the Navier-Stokes equation. In a first step the authors show the existence of a Nash equilibrium for every given leader control. Then, it is shown, under appropriate hypotheses, that there exists a leader control and an associated Nash equilibrium for the two followers such that the associated state is arbitrarily small.
reviewed by: Nicolae Cîndea
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 35G20
Mathematics Subject Classification ID: 93A13
Mathematics Subject Classification ID: 93B05
zbMATH DE Number: 7879412
zbMATH Keywords: null controllability
zbMATH Keywords: Burgers equation
zbMATH Keywords: Carleman inequalities
zbMATH Keywords: Stackelberg-Nash strategy
MaRDI profile type: Publication
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DOI: 10.1007/S00028-024-00952-Z
description: scientific article; zbMATH DE number 7879412