Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games
Journal article
Authors | Drăgan, Vasile, Ivanov, Ivan Ganchev, Popa, Ioan-Lucian and Bagdasar, Ovidiu |
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Abstract | In this paper, we examine a sampled-data Nash equilibrium strategy for a stochastic linear quadratic (LQ) differential game, in which admissible strategies are assumed to be constant on the interval between consecutive measurements. Our solution first involves transforming the problem into a linear stochastic system with finite jumps. This allows us to obtain necessary and sufficient conditions assuring the existence of a sampled-data Nash equilibrium strategy, extending earlier results to a general context with more than two players. Furthermore, we provide a numerical algorithm for calculating the feedback matrices of the Nash equilibrium strategies. Finally, we illustrate the effectiveness of the proposed algorithm by two numerical examples. As both situations highlight a stabilization effect, this confirms the efficiency of our approach. |
Keywords | General Mathematics; Engineering (miscellaneous); Computer Science (miscellaneous) |
Year | 2021 |
Journal | Mathematics |
Journal citation | 9 (21), p. 2713 |
Publisher | MDPI AG |
ISSN | 2227-7390 |
Digital Object Identifier (DOI) | https://doi.org/10.3390/math9212713 |
Web address (URL) | http://hdl.handle.net/10545/626097 |
https://creativecommons.org/licenses/by/4.0/ | |
hdl:10545/626097 | |
Publication dates | 26 Oct 2021 |
Publication process dates | |
Deposited | 10 Nov 2021, 16:22 |
Accepted | 20 Oct 2021 |
Series | Special Issue: Dynamical Systems in Engineering |
Contributors | Romanian Academy, Bucharest, Romania, The Academy of the Romanian Scientists, Bucharest, Romania, Sofia University St. Kliment Ohridski, Bulgaria, University of Alba Iulia, Romania and University of Derby |
File | File Access Level Open |
File | File Access Level Open |
https://repository.derby.ac.uk/item/93yw8/closed-loop-nash-equilibrium-in-the-class-of-piecewise-constant-strategies-in-a-linear-state-feedback-form-for-stochastic-lq-games
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