Volume 24, Number 4, October–December 2018
|Page(s)||1789 - 1813|
|Published online||13 March 2019|
Dynamic boundary control games with networks of strings
Friedrich-Alexander Universität Erlangen-Nürnberg (FAU), Department Mathematik,
2 RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany
* Corresponding author: email@example.com
Accepted: 14 December 2017
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.
Mathematics Subject Classification: 49N70 / 91A23
Key words: Vibrating string / boundary control / network / Nash equilibrium / game / pipeline network / gas transport
© EDP Sciences, SMAI 2019
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