A Game—Theoretic Model for a Stochastic Linear Quadratic Tracking Problem
In this paper, we solve a stochastic linear quadratic tracking problem. The controlled dynamical system is modeled by a system of linear Itô differential equations subject to jump Markov perturbations. We consider the case when there are two decision-makers and each of them wants to minimize the dev...
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| 格式: | Article |
| 語言: | English |
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MDPI AG
2023-01-01
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| 叢編: | Axioms |
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| 在線閱讀: | https://www.mdpi.com/2075-1680/12/1/76 |
| _version_ | 1827628593540235264 |
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| author | Vasile Drăgan Ivan Ganchev Ivanov Ioan-Lucian Popa |
| author_facet | Vasile Drăgan Ivan Ganchev Ivanov Ioan-Lucian Popa |
| author_sort | Vasile Drăgan |
| collection | DOAJ |
| description | In this paper, we solve a stochastic linear quadratic tracking problem. The controlled dynamical system is modeled by a system of linear Itô differential equations subject to jump Markov perturbations. We consider the case when there are two decision-makers and each of them wants to minimize the deviation of a preferential output of the controlled dynamical system from a given reference signal. We assume that the two decision-makers do not cooperate. Under these conditions, we state the considered tracking problem as a problem of finding a Nash equilibrium strategy for a stochastic differential game. Explicit formulae of a Nash equilibrium strategy are provided. To this end, we use the solutions of two given terminal value problems (TVPs). The first TVP is associated with a hybrid system formed by two backward nonlinear differential equations coupled by two algebraic nonlinear equations. The second TVP is associated with a hybrid system formed by two backward linear differential equations coupled by two algebraic linear equations. |
| first_indexed | 2024-03-09T13:35:40Z |
| format | Article |
| id | doaj.art-0135bcdec2b340c2931b6c0eea0ca5f7 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T13:35:40Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-0135bcdec2b340c2931b6c0eea0ca5f72023-11-30T21:11:58ZengMDPI AGAxioms2075-16802023-01-011217610.3390/axioms12010076A Game—Theoretic Model for a Stochastic Linear Quadratic Tracking ProblemVasile Drăgan0Ivan Ganchev Ivanov1Ioan-Lucian Popa2“Simion Stoilow” Institute of Mathematics, Romanian Academy, P.O. Box 1-764, 014700 Bucharest , RomaniaFaculty of Economics and Business Administration, Sofia University “St. Kl. Ohridski”, 125 Tzarigradsko Chaussee Blvd., bl. 3, 1113 Sofia, BulgariaDepartment of Computing, Mathematics and Electronics, Faculty of Computing and Engineering, “1 Decembrie 1918” University of Alba Iulia, 510009 Abla Iulia, RomaniaIn this paper, we solve a stochastic linear quadratic tracking problem. The controlled dynamical system is modeled by a system of linear Itô differential equations subject to jump Markov perturbations. We consider the case when there are two decision-makers and each of them wants to minimize the deviation of a preferential output of the controlled dynamical system from a given reference signal. We assume that the two decision-makers do not cooperate. Under these conditions, we state the considered tracking problem as a problem of finding a Nash equilibrium strategy for a stochastic differential game. Explicit formulae of a Nash equilibrium strategy are provided. To this end, we use the solutions of two given terminal value problems (TVPs). The first TVP is associated with a hybrid system formed by two backward nonlinear differential equations coupled by two algebraic nonlinear equations. The second TVP is associated with a hybrid system formed by two backward linear differential equations coupled by two algebraic linear equations.https://www.mdpi.com/2075-1680/12/1/76linear quadratic tracking problemstochastic linear differential gamesNash equilibria |
| spellingShingle | Vasile Drăgan Ivan Ganchev Ivanov Ioan-Lucian Popa A Game—Theoretic Model for a Stochastic Linear Quadratic Tracking Problem Axioms linear quadratic tracking problem stochastic linear differential games Nash equilibria |
| title | A Game—Theoretic Model for a Stochastic Linear Quadratic Tracking Problem |
| title_full | A Game—Theoretic Model for a Stochastic Linear Quadratic Tracking Problem |
| title_fullStr | A Game—Theoretic Model for a Stochastic Linear Quadratic Tracking Problem |
| title_full_unstemmed | A Game—Theoretic Model for a Stochastic Linear Quadratic Tracking Problem |
| title_short | A Game—Theoretic Model for a Stochastic Linear Quadratic Tracking Problem |
| title_sort | game theoretic model for a stochastic linear quadratic tracking problem |
| topic | linear quadratic tracking problem stochastic linear differential games Nash equilibria |
| url | https://www.mdpi.com/2075-1680/12/1/76 |
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