TY - JOUR A1 - Gugat, Martin A1 - Steffensen, Sonja ED - Trelat, Emmanuel T1 - DYNAMIC BOUNDARY CONTROL GAMES WITH NETWORKS OF STRINGS JF - ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV) N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1051/cocv/2017082 ER - TY - JOUR A1 - Gugat, Martin A1 - Schuster, Michael A1 - Steffensen, Sonja T1 - A Dynamic Multilevel Model of the European Gas Market N2 - The European gas market is governed by rules that are agreed on by the European Union. We present a mathematical market model that takes into account this structure, where the technical system operator (TSO) offers certain transportation capacities that can be booked and later nominated within the previously chosen bookings. The TSO also fixes booking fees and defines an operational control of the gas pipeline system in order to deliver the gas according to the nominations. Since the gas flow is governed by a system of partial differential equations, to realize this control structure partial differential equations (PDEs) should be involved in the model. While the four level gas market model has been discussed previously, in this paper we take into account the flow model by PDEs in the discussion of the model and in the reduction to a single level problem, where we also state the corresponding necessary optimality conditions. KW - Gas Dynamics KW - Gas Market KW - Nodal Control KW - Isothermal Euler Equations Y1 - 2022 UR - http://cot.mathres.org/archives/1488 IS - Volume 2023 SP - 1 EP - 26 PB - Communications in Optimization Theory ER -