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 cost

Rosario Maggistro;
2020-01-01

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
5
File in questo prodotto:
File Dimensione Formato  
Bagagiolo_Maggistro_Zoppello_revised2 (1).pdf

non disponibili

Tipologia: Documento in Pre-print
Licenza: Accesso chiuso-personale
Dimensione 486.25 kB
Formato Adobe PDF
486.25 kB Adobe PDF   Visualizza/Apri

I documenti in ARCA 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/10278/3724501
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? ND
social impact