A Zero-Sum Deterministic Impulse Controls Game in Infinite Horizon with a New HJBI QVI
Optimization and Control
2021-01-29 v1
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.
Keywords
Cite
@article{arxiv.2101.11669,
title = {A Zero-Sum Deterministic Impulse Controls Game in Infinite Horizon with a New HJBI QVI},
author = {Brahim El Asri and Hafid Lalioui and Sehail Mazid},
journal= {arXiv preprint arXiv:2101.11669},
year = {2021}
}