Robust Dynamic Programming in N Players Uncertain Differential Games
In this paper we consider a non-cooperative N players differential game affected by deterministic uncertainties. Sufficient conditions for the existence of a robust feedback Nash equilibrium are presented in a set of min-max forms of Hamilton–Jacobi–Bellman equations. Such conditions are then used t...
| Autores principales: | , , , |
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| Formato: | Artículo |
| Lenguaje: | inglés |
| Publicado: |
Vilnius University
2020
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| Materias: | |
| Acceso en línea: | http://eprints.uanl.mx/25056/1/43.pdf |
| _version_ | 1824420072680062976 |
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| author | Jiménez Lizárraga, Manuel Rodríguez Sánchez, Sara V. De la Cruz, Naín Villarreal, César Emilio |
| author_facet | Jiménez Lizárraga, Manuel Rodríguez Sánchez, Sara V. De la Cruz, Naín Villarreal, César Emilio |
| author_sort | Jiménez Lizárraga, Manuel |
| collection | Repositorio Institucional |
| description | In this paper we consider a non-cooperative N players differential game affected by deterministic uncertainties. Sufficient conditions for the existence of a robust feedback Nash equilibrium are presented in a set of min-max forms of Hamilton–Jacobi–Bellman equations. Such conditions are then used to find the robust Nash controls for a linear affine quadratic game affected by a square integrable uncertainty, which is seen as a malicious fictitious player trying to maximize the cost function of each player. The approach allows us to find robust strategies in the solution of a group of coupled Riccati differential equation. The finite, as well as infinite, time horizon cases are solved for
this last game. As an illustration of the approach, the problem of the coordination of a two-echelon supply chain with seasonal uncertain fluctuations in demand is developed |
| format | Article |
| id | eprints-25056 |
| institution | UANL |
| language | English |
| publishDate | 2020 |
| publisher | Vilnius University |
| record_format | eprints |
| spelling | eprints-250562023-03-03T18:54:32Z http://eprints.uanl.mx/25056/ Robust Dynamic Programming in N Players Uncertain Differential Games Jiménez Lizárraga, Manuel Rodríguez Sánchez, Sara V. De la Cruz, Naín Villarreal, César Emilio QA Matemáticas, Ciencias computacionales In this paper we consider a non-cooperative N players differential game affected by deterministic uncertainties. Sufficient conditions for the existence of a robust feedback Nash equilibrium are presented in a set of min-max forms of Hamilton–Jacobi–Bellman equations. Such conditions are then used to find the robust Nash controls for a linear affine quadratic game affected by a square integrable uncertainty, which is seen as a malicious fictitious player trying to maximize the cost function of each player. The approach allows us to find robust strategies in the solution of a group of coupled Riccati differential equation. The finite, as well as infinite, time horizon cases are solved for this last game. As an illustration of the approach, the problem of the coordination of a two-echelon supply chain with seasonal uncertain fluctuations in demand is developed Vilnius University 2020 Article PeerReviewed text en cc_by_nc_nd http://eprints.uanl.mx/25056/1/43.pdf http://eprints.uanl.mx/25056/1.haspreviewThumbnailVersion/43.pdf Jiménez Lizárraga, Manuel y Rodríguez Sánchez, Sara V. y De la Cruz, Naín y Villarreal, César Emilio (2020) Robust Dynamic Programming in N Players Uncertain Differential Games. Informática, 31 (4). pp. 769-791. ISSN 1822-8844 https://informatica.vu.lt/journal/INFORMATICA |
| spellingShingle | QA Matemáticas, Ciencias computacionales Jiménez Lizárraga, Manuel Rodríguez Sánchez, Sara V. De la Cruz, Naín Villarreal, César Emilio Robust Dynamic Programming in N Players Uncertain Differential Games |
| thumbnail | https://rediab.uanl.mx/themes/sandal5/images/online.png |
| title | Robust Dynamic Programming in N Players Uncertain Differential Games |
| title_full | Robust Dynamic Programming in N Players Uncertain Differential Games |
| title_fullStr | Robust Dynamic Programming in N Players Uncertain Differential Games |
| title_full_unstemmed | Robust Dynamic Programming in N Players Uncertain Differential Games |
| title_short | Robust Dynamic Programming in N Players Uncertain Differential Games |
| title_sort | robust dynamic programming in n players uncertain differential games |
| topic | QA Matemáticas, Ciencias computacionales |
| url | http://eprints.uanl.mx/25056/1/43.pdf |
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