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Open Loop Robust Equilibria in Uncertain Discrete Time Games

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  • Control Theory and Applications
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Abstract

This paper tackles the problem of a discrete time N players game affected by some sort of time-varying uncertain perturbation. The philosophy of the uncertainty worst case scenario with respect to the i-player is developed to derive necessary and sufficient conditions for the existence of an Open Loop Robust Nash Equilibria. Such conditions are presented in terms of the solvability of a set of discrete time Riccati type equations with some boundary conditions. As an illustration of the solution, a simulation of the coordination of a two-echelon supply chain with uncertain seasonal fluctuations in the demand is developed.

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Authors and Affiliations

  1. Faculty of Physical and Mathematical Sciences, Universidad Autónoma de Nuevo León, Pedro de Alba s/n, Cd. Universitaria, San Nicolás de los Garza, Nuevo León, México

    Fernando Guerrero Vélez, Manuel Jiménez Lizárraga & Celeste Rodriguez Carreon

Authors
  1. Fernando Guerrero Vélez
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  2. Manuel Jiménez Lizárraga
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  3. Celeste Rodriguez Carreon
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Correspondence to Manuel Jiménez Lizárraga.

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Recommended by Associate Editor M. Chadli under the direction of Editor Jessie (Ju H.) Park.

Fernando Guerrero Vélez received his B.S. degree in physics from Autonomous University of Nuevo León in 2012 and an M.S. degree from CIIIA-UANL in 2015. He is currently a Ph.D. student at CICFIM-UANL, México. His research interests include unmanned aerial vehicles, game theory, adaptive control, and dynamic systems.

Manuel Jiménez Lizárraga received his B.S. degree in electrical engineering from Instituto Tecnologico de Culiacán, México, an M.S. and a Ph.D. degrees in automatic control from CINVESTAV-IPN México, in 1996, 2000, and 2006, respectively. He is currently with the Faculty of Physical and Mathematical Sciences of Autonomous University of Nuevo León, México. His research interests include uncertain differential games, robust and optimal control, and sliding mode observers.

Celeste Rodriguez Carreon received her B.S. degree in mathematics in 2008, and a Ph.D. degree in industrial physics engineering in 2013 at the Faculty of Physics and Mathematics Science from the Autonomous University of Nuevo Leon, Mexico. She is currently at the same faculty. Her research interests include differential games, stochastic systems, and robust control problems.

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Vélez, F.G., Lizárraga, M.J. & Carreon, C.R. Open Loop Robust Equilibria in Uncertain Discrete Time Games. Int. J. Control Autom. Syst. 19, 587–595 (2021). https://doi.org/10.1007/s12555-020-0027-3

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  • DOI: https://doi.org/10.1007/s12555-020-0027-3

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