DYNAMIC BOUNDARY CONTROL GAMES WITH NETWORKS OF STRINGS

Gugat M, Steffensen S (2018)

Publication Type: Journal article

Publication year: 2018

Journal

Esaim-Control Optimisation and Calculus of Variations EDP Sciences

Book Volume: 24

Pages Range: 1789-1813

Journal Issue: 4

DOI: 10.1051/cocv/2017082

Abstract

Consider a star-shaped network of strings. Each string is governed by the wave equation. At each boundary node of the network there is a player that performs Dirichlet boundary control action and in this way influences the system state. At the central node, the states are coupled by algebraic conditions in such a way that the energy is conserved. We consider the corresponding antagonistic game where each player minimizes a certain quadratic objective function that is given by the sum of a control cost and a tracking term for the final state. We prove that under suitable assumptions a unique Nash equilibrium exists and give an explicit representation of the equilibrium strategies.

Authors with CRIS profile

Martin Gugat Lehrstuhl für Angewandte Mathematik

Involved external institutions

Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen DE Germany (DE)

How to cite

APA:

Gugat, M., & Steffensen, S. (2018). DYNAMIC BOUNDARY CONTROL GAMES WITH NETWORKS OF STRINGS. Esaim-Control Optimisation and Calculus of Variations, 24(4), 1789-1813. https://dx.doi.org/10.1051/cocv/2017082

MLA:

Gugat, Martin, and Sonja Steffensen. "DYNAMIC BOUNDARY CONTROL GAMES WITH NETWORKS OF STRINGS." Esaim-Control Optimisation and Calculus of Variations 24.4 (2018): 1789-1813.

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