On class of linear quadratic non-cooperative differential games with continuous updating

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9 Scopus citations

Abstract

The subject of this paper is a linear quadratic case of a differential game model with continuous updating. This class of differential games is essentially new, there it is assumed that at each time instant, players have or use information about the game structure defined on a closed time interval with a fixed duration. As time goes on, information about the game structure updates. Under the information about the game structure we understand information about motion equations and payoff functions of players. A linear quadratic case for this class of games is particularly important for practical problems arising in the engineering of human-machine interaction. The notion of Nash equilibrium as an optimality principle is defined and the explicit form of Nash equilibrium for the linear quadratic case is presented. Also, the case of dynamic updating for the linear quadratic differential game is studied and uniform convergence of Nash equilibrium strategies and corresponding trajectory for a case of continuous updating and dynamic updating is demonstrated.

Original languageEnglish
Title of host publicationMathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Proceedings
EditorsMichael Khachay, Yury Kochetov, Panos Pardalos
PublisherSpringer Nature
Pages635-650
Number of pages16
ISBN (Print)9783030226282
DOIs
StatePublished - 1 Jan 2019
Event18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019 - Ekaterinburg, Russian Federation
Duration: 8 Jul 201912 Jul 2019

Publication series

NameLecture Notes in Computer Science
PublisherSPRINGER INTERNATIONAL PUBLISHING AG
Volume11548
ISSN (Print)0302-9743

Conference

Conference18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019
Country/TerritoryRussian Federation
CityEkaterinburg
Period8/07/1912/07/19

Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Keywords

  • Differential games with continuous updating
  • Linear quadratic differential games
  • Nash equilibrium

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