Approximation of value function of differential game with minimal cost
Affiliation:
1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences; Ural Federal University
Abstract
The paper is concerned with the approximation of the value function of the zero-sum differential game with the minimal cost, i.e., the differential game with the payoff functional determined by the minimization of some quantity along the trajectory by the solutions of continuous-time stochastic games with the stopping governed by one player. Notice that the value function of the auxiliary continuous-time stochastic game is described by the Isaacs–Bellman equation with additional inequality constraints. The Isaacs–Bellman equation is a parabolic PDE for the case of stochastic differential game and it takes a form of system of ODEs for the case of continuous-time Markov game. The approximation developed in the paper is based on the concept of the stochastic guide first proposed by Krasovskii and Kotelnikova.
Funder
Russian Science Foundation
Publisher
Udmurt State University
Subject
Fluid Flow and Transfer Processes,General Mathematics,General Computer Science
Cited by
1 articles.
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1. Zero-Sum Continuous-Time Markov Games with One-Side Stopping;Journal of the Operations Research Society of China;2023-11-07