DYNAMIC BOUNDARY CONTROL GAMES WITH NETWORKS OF STRINGS
- 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.
Author: | Martin Gugat, Sonja Steffensen |
---|---|
DOI: | https://doi.org/10.1051/cocv/2017082 |
Parent Title (English): | ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV) |
Editor: | Emmanuel Trelat |
Document Type: | Article |
Language: | English |
Date of Publication (online): | 2018/01/19 |
Date of first Publication: | 2018/01/19 |
Release Date: | 2018/01/19 |
Subprojects: | C03 |