Necessary conditions for constant solutions of coupled Riccati equations in Nash games
type: Item
instance of: scholarly article
title: Necessary conditions for constant solutions of coupled Riccati equations in Nash games
zbMATH Open document ID: 0805.90133
DOI: 10.1016/0167-6911(93)90072-E
published in: Systems \& Control Letters
publication date: 1994-03-24T00:00:00Z
review text: The well-known theorem concerning open-loop linear-quadratic. Nash games states that under appropriate assumptions the corresponding open-loop controls can be constructed by explicit formulae, which contain the solution of coupled Riccati-type differential matrix equations (RDE). The purpose of the reviewed paper is to study the asymptotic behaviour of the mentioned matrix solution, as the time interval tends to infinity. For this purpose the corresponding obtained from RDE by replacing therein the derivatives by the zero matrices. Then conditions for the existence of solutions of ARE and assumptions under which the solution of (RDE) converges to the solution of (ARE) are derived. The estimate for the rate of convergence is obtained. Two examples illustrate the results.
Mathematics Subject Classification ID: 91A23
zbMATH DE Number: 516809
zbMATH Keywords: Nash games
zbMATH Keywords: coupled Riccati-type differential matrix equations
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: rate of convergence
author: Hisham Abou-Kandil
author: Gerhard Freiling
author: G. Jank
reviewed by: O. I. Nikonov
MaRDI profile type: Publication
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full work available at URL: 0167-6911(93)90072-e
OpenAlex ID: W2063445935
description: scientific article; zbMATH DE number 516809