TY - JOUR

T1 - Control systems of interacting objects modeled as a game against nature under a mean field approach

AU - Higuera-Chan, Carmen G.

AU - Jasso-Fuentes, Héctor

AU - Minjárez-Sosa, J. Adolfo

N1 - Publisher Copyright:
© 2017, American Institute of Mathematical Sciences.

PY - 2017

Y1 - 2017

N2 - This paper deals with discrete-time stochastic systems composed of a large number of N interacting objects (a.k.a. agents or particles). There is a central controller whose decisions, at each stage, affect the system behavior. Each object evolves randomly among a finite set of classes, according to a transition law which depends on an unknown parameter. Such a parameter is possibly non observable and may change from stage to stage. Due to the lack of information and to the large number of agents, the control problem under study is rewritten as a game against nature according to the mean field theory; that is, we introduce a game model associated to the proportions of the objects in each class, whereas the values of the unknown parameter are now considered as "actions" selected by an opponent to the controller (the nature). Then, letting N → ∞ (the mean field limit) and considering a discounted optimality criterion, the objective for the controller is to minimize the maximum cost, where the maximum is taken over all possible strategies of the nature.

AB - This paper deals with discrete-time stochastic systems composed of a large number of N interacting objects (a.k.a. agents or particles). There is a central controller whose decisions, at each stage, affect the system behavior. Each object evolves randomly among a finite set of classes, according to a transition law which depends on an unknown parameter. Such a parameter is possibly non observable and may change from stage to stage. Due to the lack of information and to the large number of agents, the control problem under study is rewritten as a game against nature according to the mean field theory; that is, we introduce a game model associated to the proportions of the objects in each class, whereas the values of the unknown parameter are now considered as "actions" selected by an opponent to the controller (the nature). Then, letting N → ∞ (the mean field limit) and considering a discounted optimality criterion, the objective for the controller is to minimize the maximum cost, where the maximum is taken over all possible strategies of the nature.

KW - Discounted criterion

KW - Games against nature

KW - Mean field theory

KW - Minimax control

KW - Systems of interacting objects

UR - http://www.scopus.com/inward/record.url?scp=85044327829&partnerID=8YFLogxK

U2 - 10.3934/jdg.2017004

DO - 10.3934/jdg.2017004

M3 - Artículo

SN - 2164-6074

VL - 4

SP - 59

EP - 74

JO - Journal of Dynamics and Games

JF - Journal of Dynamics and Games

IS - 1

ER -