Work

Differential Games for a Mixed ODE-PDE System

Year: 2025

Type: article

Abstract: . Motivated by a vaccination coverage problem, we consider here a zero-sum differential game governed by a differential system consisting of a hyperbolic partial differential equation (PDE) and an ordinary differential equation (ODE). Two players act through their respective controls to influence the evolution of the system with the aim of minimizing their objective functionals [Formula: see text] and [Formula: see text], under the assumption that [Formula: see text]. First we prove a well-posedness and a stability result for the differential system, once the control functions are fixed. Then we introduce the concept of nonanticipating strategies for both players, and we consider the associated value functions, which solve two infinite-dimensional Hamilton–Jacobi–Isaacs equations in the viscosity sense.

Source: SIAM Journal on Control and Optimization

DOI: 10.1137/24m1699760

Authors: Mauro Garavello, Elena Rossi, Abraham Sylla

Institutions: University of Milano-Bicocca, University of Modena and Reggio Emilia, Centre National de la Recherche Scientifique, Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, Université de Picardie Jules Verne

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni