Geodesic
Dynamic boundary control games with networks of strings
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 4, pp. 1789-1813

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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.

DOI : 10.1051/cocv/2017082
Classification : 49N70, 91A23
Keywords: Vibrating string, boundary control, network, Nash equilibrium, game, pipeline network, gas transport

Gugat, Martin 1 ; Steffensen, Sonja 1

1 
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     title = {Dynamic boundary control games with networks of strings},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1789--1813},
     publisher = {EDP-Sciences},
     volume = {24},
     number = {4},
     year = {2018},
     doi = {10.1051/cocv/2017082},
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     mrnumber = {3922441},
     language = {en},
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Gugat, Martin; Steffensen, Sonja. Dynamic boundary control games with networks of strings. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 4, pp. 1789-1813. doi: 10.1051/cocv/2017082

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