Deterministic Differential Games in Infinite Horizon Involving Continuous and Impulse Controls

2021/07/07 by Brahim El Asri, Asri, Brahim El, Hafid Lalioui +1
Computer Science · Economics, Econometrics and Finance · #Continuous-impulse controls #DPP #Differential game #Economic theories and models #FOS: Mathematics #HJBI quasi-variational inequalities #Infinite horizon #Isaacs condition #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stochastic processes and financial applications #Viscosity solutions

paper · pdf · doi:10.48550/arxiv.2107.03524

openalex publication_date 2021/07/07 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28

Abstract

We consider a two-player zero-sum deterministic differential game where each player uses both continuous and impulse controls in infinite-time horizon. We assume that the impulses supposed to be of general term and the costs depend on the state of the system. We use the dynamic programming principle and viscosity solutions approach to show existence and uniqueness of a solution for the Hamilton-Jacobi-Bellman-Isaacs (HJBI) partial differential equations (PDEs) of the game. We prove under Isaacs condition that the upper and lower value functions coincide.

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