A Zero-Sum Deterministic Impulse Controls Game in Infinite Horizon with a New HJBI QVI

2021/01/27 by Brahim El Asri, Asri, Brahim El, Hafid Lalioui +3
Computer Science · Mathematics · #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2101.11669

openalex publication_date 2021/01/27 · openalex created_date 2023/08/19 · openalex updated_date 2026/07/28

Abstract

In the present paper, we study a two-player zero-sum deterministic differential game with both players adopting impulse controls, in infinite time horizon, under rather weak assumptions on the cost functions. We prove by means of the dynamic programming principle (DPP) that the lower and upper value functions are continuous and viscosity solutions to the corresponding Hamilton-Jacobi-Bellman-Isaacs (HJBI) quasi-variational inequality (QVI). We define a new HJBI QVI for which, under a proportional property assumption on the maximizer cost, the value functions are the unique viscosity solution. We then prove that the lower and upper value functions coincide.

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