Multi-time scale zero-sum differential games with perfect state measurements
type: Item
instance of: scholarly article
title: Multi-time scale zero-sum differential games with perfect state measurements
zbMATH Open document ID: 0830.90145
DOI: 10.1007/BF01968532
author: Zigang Pan
author: Tamer Başar
published in: Dynamics and Control
publication date: 1996-01-30T00:00:00Z
review text: The paper is devoted to three multi-time scale zero-sum differential games. Its open-loop dynamics are described by a singularly perturbed differential equation which depends on two small positive parameters \(\varepsilon_1\), \(\varepsilon_2\). Given a quadratic cost functional, to be minimized the Player 1 and maximized by Player 2, for each fixed \(\varepsilon_1\), \(\varepsilon_2\) the well-known approach based on a generalized Riccati equation can be used. However, its realization for small values of the above parameters is prone to numerical errors and inaccuracies. The notion of ``approximate saddle- point solution'' is used in the paper to refer to strategies that do not depend on \(\varepsilon_1\) and \(\varepsilon_2\), while providing cost levels within \(O(\varepsilon_1)\) of the full-order game. Necessary and sufficient conditions for the existence of such ``approximate'' solutions are obtained. It is shown that the original game can be decomposed into three subgames -- slow, fast and fastest -- the composite solution of which make up the approximate saddle-point solution of the original game.
Mathematics Subject Classification ID: 91A23
Mathematics Subject Classification ID: 91A60
Mathematics Subject Classification ID: 93C70
zbMATH DE Number: 729845
zbMATH Keywords: approximate saddle-point solution
zbMATH Keywords: multi-time scale zero-sum differential games
reviewed by: O. I. Nikonov
MaRDI profile type: Publication
cites work: Dynamic noncooperative game theory
cites work: \(H^ \infty\) - optimal control and related minimax design problems. A dynamic game approach
cites work: \(H^ \infty\)-optimal control for singularly perturbed systems. I: Perfect state measurements
cites work: A decomposition of near-optimum regulators for systems with slow and fast modes
cites work: Q4309840
cites work: Multiparameter singular perturbations of linear systems with multiple time scales
full work available at URL: https://doi.org/10.1007/bf01968532
OpenAlex ID: W2172860406
description: scientific article; zbMATH DE number 729845