Geodesic
A Hybrid Differential Game with Switching Thermostatic-Type Dynamics and Costs
Minimax theory and its applications, Tome 5 (2020) no. 2
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We consider an infinite horizon zero-sum differential game where the dynamics of each player and the running costs depend on the evolution of some discrete (switching) variables. In particular, such switching variables evolve according to the switching law of a so-called thermostatic delayed relay, applied to the players’ states. We first address the problem of the continuity of both lower and upper value function. Then, by a suitable representation of the problem as a coupling of several exit-time differential games, we characterize those value functions as, respectively, the unique solution of a coupling of several Dirichlet problems for Hamilton-Jacobi-Isaacs equations. The concept of viscosity solutions and a suitable definition of boundary conditions in the viscosity sense are used in the paper.
Mots-clés : Differential games, hybrid systems, switching, exit costs, Hamilton-Jacobi-Isaacs equations, viscosity solutions, non-anticipating strategies, delayed thermostat 
@article{MTA_2020_5_2_a1,
     author = {Fabio Bagagiolo,Rosario Maggistro,Marta Zoppello},
     title = {A {Hybrid} {Differential} {Game} with {Switching} {Thermostatic-Type} {Dynamics} and {Costs}},
     journal = {Minimax theory and its applications},
     year = {2020},
     volume = {5},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/MTA_2020_5_2_a1/}
}
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Fabio Bagagiolo,Rosario Maggistro,Marta Zoppello. A Hybrid Differential Game with Switching Thermostatic-Type Dynamics and Costs. Minimax theory and its applications, Tome 5 (2020) no. 2. http://geodesic.mathdoc.fr/item/MTA_2020_5_2_a1/