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Article

Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games

1
“Simion Stoilow” Institute of Mathematics, Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania
2
The Academy of the Romanian Scientists, Str. Ilfov, 3, 050044 Bucharest, Romania
3
Faculty of Economics and Business Administration, Sofia University St. Kliment Ohridski, 1113 Sofia, Bulgaria
4
Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
5
School of Computing and Engineering, University of Derby, Derby DE22 1GB, UK
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Ioannis Dassios
Mathematics 2021, 9(21), 2713; https://doi.org/10.3390/math9212713
Received: 7 September 2021 / Revised: 15 October 2021 / Accepted: 20 October 2021 / Published: 26 October 2021
(This article belongs to the Special Issue Dynamical Systems in Engineering)
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. View Full-Text
Keywords: nash equilibria; stochastic LQ differential games; sampled-data controls; equilibrium strategies; optimal trajectories nash equilibria; stochastic LQ differential games; sampled-data controls; equilibrium strategies; optimal trajectories
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MDPI and ACS Style

Drăgan, V.; Ivanov, I.G.; Popa, I.-L.; Bagdasar, O. Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games. Mathematics 2021, 9, 2713. https://doi.org/10.3390/math9212713

AMA Style

Drăgan V, Ivanov IG, Popa I-L, Bagdasar O. Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games. Mathematics. 2021; 9(21):2713. https://doi.org/10.3390/math9212713

Chicago/Turabian Style

Drăgan, Vasile, Ivan G. Ivanov, Ioan-Lucian Popa, and Ovidiu Bagdasar. 2021. "Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games" Mathematics 9, no. 21: 2713. https://doi.org/10.3390/math9212713

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