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Non-autonomous linear quadratic non-cooperative differential games with continuous updating
Ildus Kuchkarova, Ovanes Petrosianab, Yin Liac a St. Petersburg State University, Faculty of Applied Mathematics and Control Processes, 7/9, Universitetskaya nab., St. Petersburg, 199034, Russia
b HSE University, 20, Myasnitskaya ul., St. Petersburg, 194100, Russia
c School of Mathematics, Harbin Institute of Technology, 92, West Dazhi St., Harbin, 15000, China
Аннотация:
The subject of this paper is a non-autonomous linear quadratic case of a differential game model with continuous updating. This class of differential games is essentially new where 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. During the interval information about motion equations and payoff functions of players updates. It is non-autonomy that simulates this effect of updating information. A linear quadratic case for this class of games is particularly important for practical problems arising in the engineering of human-machine interaction. Here we define the Nash equilibrium as an optimality principle and present an explicit form of Nash equilibrium for the linear quadratic case. 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.
Ключевые слова:
differential games with continuous updating, Nash equilibrium, linear quadratic differential games, non-autonomous.
Образец цитирования:
Ildus Kuchkarov, Ovanes Petrosian, Yin Li, “Non-autonomous linear quadratic non-cooperative differential games with continuous updating”, Contributions to Game Theory and Management, 15 (2022), 132–154
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/cgtm420 https://www.mathnet.ru/rus/cgtm/v15/p132
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