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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Autor*in:	Vasile Drăgan [verfasserIn] Ivan Ganchev Ivanov [verfasserIn] Ioan-Lucian Popa [verfasserIn] Ovidiu Bagdasar [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	nash equilibria stochastic LQ differential games sampled-data controls equilibrium strategies optimal trajectories

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 9(2021), 21, p 2713
Übergeordnetes Werk:	volume:9 ; year:2021 ; number:21, p 2713

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/math9212713

Katalog-ID:	DOAJ061098493

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spelling	10.3390/math9212713 doi (DE-627)DOAJ061098493 (DE-599)DOAJ689f5191224a4904b41f4b332aba0a1c DE-627 ger DE-627 rakwb eng QA1-939 Vasile Drăgan verfasserin aut Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. nash equilibria stochastic LQ differential games sampled-data controls equilibrium strategies optimal trajectories Mathematics Ivan Ganchev Ivanov verfasserin aut Ioan-Lucian Popa verfasserin aut Ovidiu Bagdasar verfasserin aut In Mathematics MDPI AG, 2013 9(2021), 21, p 2713 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:9 year:2021 number:21, p 2713 https://doi.org/10.3390/math9212713 kostenfrei https://doaj.org/article/689f5191224a4904b41f4b332aba0a1c kostenfrei https://www.mdpi.com/2227-7390/9/21/2713 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2021 21, p 2713
allfields_unstemmed	10.3390/math9212713 doi (DE-627)DOAJ061098493 (DE-599)DOAJ689f5191224a4904b41f4b332aba0a1c DE-627 ger DE-627 rakwb eng QA1-939 Vasile Drăgan verfasserin aut Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. nash equilibria stochastic LQ differential games sampled-data controls equilibrium strategies optimal trajectories Mathematics Ivan Ganchev Ivanov verfasserin aut Ioan-Lucian Popa verfasserin aut Ovidiu Bagdasar verfasserin aut In Mathematics MDPI AG, 2013 9(2021), 21, p 2713 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:9 year:2021 number:21, p 2713 https://doi.org/10.3390/math9212713 kostenfrei https://doaj.org/article/689f5191224a4904b41f4b332aba0a1c kostenfrei https://www.mdpi.com/2227-7390/9/21/2713 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2021 21, p 2713
allfieldsGer	10.3390/math9212713 doi (DE-627)DOAJ061098493 (DE-599)DOAJ689f5191224a4904b41f4b332aba0a1c DE-627 ger DE-627 rakwb eng QA1-939 Vasile Drăgan verfasserin aut Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. nash equilibria stochastic LQ differential games sampled-data controls equilibrium strategies optimal trajectories Mathematics Ivan Ganchev Ivanov verfasserin aut Ioan-Lucian Popa verfasserin aut Ovidiu Bagdasar verfasserin aut In Mathematics MDPI AG, 2013 9(2021), 21, p 2713 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:9 year:2021 number:21, p 2713 https://doi.org/10.3390/math9212713 kostenfrei https://doaj.org/article/689f5191224a4904b41f4b332aba0a1c kostenfrei https://www.mdpi.com/2227-7390/9/21/2713 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2021 21, p 2713
allfieldsSound	10.3390/math9212713 doi (DE-627)DOAJ061098493 (DE-599)DOAJ689f5191224a4904b41f4b332aba0a1c DE-627 ger DE-627 rakwb eng QA1-939 Vasile Drăgan verfasserin aut Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. nash equilibria stochastic LQ differential games sampled-data controls equilibrium strategies optimal trajectories Mathematics Ivan Ganchev Ivanov verfasserin aut Ioan-Lucian Popa verfasserin aut Ovidiu Bagdasar verfasserin aut In Mathematics MDPI AG, 2013 9(2021), 21, p 2713 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:9 year:2021 number:21, p 2713 https://doi.org/10.3390/math9212713 kostenfrei https://doaj.org/article/689f5191224a4904b41f4b332aba0a1c kostenfrei https://www.mdpi.com/2227-7390/9/21/2713 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2021 21, p 2713
language	English
source	In Mathematics 9(2021), 21, p 2713 volume:9 year:2021 number:21, p 2713
sourceStr	In Mathematics 9(2021), 21, p 2713 volume:9 year:2021 number:21, p 2713
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topic_facet	nash equilibria stochastic LQ differential games sampled-data controls equilibrium strategies optimal trajectories Mathematics
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callnumber-first	Q - Science
author	Vasile Drăgan
spellingShingle	Vasile Drăgan misc QA1-939 misc nash equilibria misc stochastic LQ differential games misc sampled-data controls misc equilibrium strategies misc optimal trajectories misc Mathematics 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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topic_title	QA1-939 Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games nash equilibria stochastic LQ differential games sampled-data controls equilibrium strategies optimal trajectories
topic	misc QA1-939 misc nash equilibria misc stochastic LQ differential games misc sampled-data controls misc equilibrium strategies misc optimal trajectories misc Mathematics
topic_unstemmed	misc QA1-939 misc nash equilibria misc stochastic LQ differential games misc sampled-data controls misc equilibrium strategies misc optimal trajectories misc Mathematics
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title	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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title_sort	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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title_auth	Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games
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.
abstractGer	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.
abstract_unstemmed	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.
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title_short	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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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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