Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games
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...
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MDPI AG
2021-10-01
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| Schriftenreihe: | Mathematics |
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| author | Vasile Drăgan Ivan Ganchev Ivanov Ioan-Lucian Popa Ovidiu Bagdasar |
| author_facet | Vasile Drăgan Ivan Ganchev Ivanov Ioan-Lucian Popa Ovidiu Bagdasar |
| author_sort | Vasile Drăgan |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T05:56:51Z |
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| id | doaj.art-689f5191224a4904b41f4b332aba0a1c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:56:51Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-689f5191224a4904b41f4b332aba0a1c2023-11-22T21:17:46ZengMDPI AGMathematics2227-73902021-10-01921271310.3390/math9212713Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ GamesVasile Drăgan0Ivan Ganchev Ivanov1Ioan-Lucian Popa2Ovidiu Bagdasar3“Simion Stoilow” Institute of Mathematics, Romanian Academy, P.O. Box 1-764, 014700 Bucharest, RomaniaFaculty of Economics and Business Administration, Sofia University St. Kliment Ohridski, 1113 Sofia, BulgariaDepartment of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, RomaniaSchool of Computing and Engineering, University of Derby, Derby DE22 1GB, UKIn 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.https://www.mdpi.com/2227-7390/9/21/2713nash equilibriastochastic LQ differential gamessampled-data controlsequilibrium strategiesoptimal trajectories |
| spellingShingle | Vasile Drăgan Ivan Ganchev Ivanov Ioan-Lucian Popa Ovidiu Bagdasar Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games Mathematics nash equilibria stochastic LQ differential games sampled-data controls equilibrium strategies optimal trajectories |
| title | Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games |
| title_full | Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games |
| title_fullStr | Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games |
| title_full_unstemmed | Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games |
| title_short | Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games |
| title_sort | closed loop nash equilibrium in the class of piecewise constant strategies in a linear state feedback form for stochastic lq games |
| topic | nash equilibria stochastic LQ differential games sampled-data controls equilibrium strategies optimal trajectories |
| url | https://www.mdpi.com/2227-7390/9/21/2713 |
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