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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Autores principales:	Vasile Drăgan, Ivan Ganchev Ivanov, Ioan-Lucian Popa, Ovidiu Bagdasar
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	nash equilibria stochastic LQ differential games sampled-data controls equilibrium strategies optimal trajectories Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/689f5191224a4904b41f4b332aba0a1c
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spelling	oai:doaj.org-article:689f5191224a4904b41f4b332aba0a1c2021-11-11T18:16:16ZClosed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games10.3390/math92127132227-7390https://doaj.org/article/689f5191224a4904b41f4b332aba0a1c2021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2713https://doaj.org/toc/2227-7390In 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.Vasile DrăganIvan Ganchev IvanovIoan-Lucian PopaOvidiu BagdasarMDPI AGarticlenash equilibriastochastic LQ differential gamessampled-data controlsequilibrium strategiesoptimal trajectoriesMathematicsQA1-939ENMathematics, Vol 9, Iss 2713, p 2713 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	nash equilibria stochastic LQ differential games sampled-data controls equilibrium strategies optimal trajectories Mathematics QA1-939
spellingShingle	nash equilibria stochastic LQ differential games sampled-data controls equilibrium strategies optimal trajectories Mathematics QA1-939 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
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.
format	article
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
title	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_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_sort	closed-loop nash equilibrium in the class of piecewise constant strategies in a linear state feedback form for stochastic lq games
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/689f5191224a4904b41f4b332aba0a1c
work_keys_str_mv	AT vasiledragan closedloopnashequilibriumintheclassofpiecewiseconstantstrategiesinalinearstatefeedbackformforstochasticlqgames AT ivanganchevivanov closedloopnashequilibriumintheclassofpiecewiseconstantstrategiesinalinearstatefeedbackformforstochasticlqgames AT ioanlucianpopa closedloopnashequilibriumintheclassofpiecewiseconstantstrategiesinalinearstatefeedbackformforstochasticlqgames AT ovidiubagdasar closedloopnashequilibriumintheclassofpiecewiseconstantstrategiesinalinearstatefeedbackformforstochasticlqgames
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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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