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.

A Hybrid Differential Game with Switching Thermostatic-Type Dynamics and Costs / Bagagiolo, Fabio; Maggistro, Rosario; Zoppello, Marta. - In: MINIMAX THEORY AND ITS APPLICATIONS. - ISSN 2199-1413. - STAMPA. - 5:2(2020), pp. 1-30.

A Hybrid Differential Game with Switching Thermostatic-Type Dynamics and Costs

Marta, Zoppello
2020

Abstract

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.
2020
File in questo prodotto:
File Dimensione Formato  
MTA.pdf

non disponibili

Descrizione: Articolo principale
Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 280.98 kB
Formato Adobe PDF
280.98 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2898060