A mean field absorbing control model for interacting objects systems
We study a class of discrete-time stochastic systems composed of a large number of N interacting objects, which are classified in a finite number of classes. The behavior of the objects is controlled by a central decision-maker as follows. At each stage, once the configuration of the system is obser...
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| Veröffentlicht in: | Discrete event dynamic systems 2021, Vol.31 (3), p.349-372 |
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| container_title | Discrete event dynamic systems |
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| creator | Elena, Martínez-Manzanares M Adolfo, Minjárez-Sosa J |
| description | We study a class of discrete-time stochastic systems composed of a large number of
N
interacting objects, which are classified in a finite number of classes. The behavior of the objects is controlled by a central decision-maker as follows. At each stage, once the configuration of the system is observed, the controller takes a decision; then a cost is incurred and there is a positive probability the process stops, otherwise the objects move randomly among the classes according to a transition probability. That is, with positive probability, the system is absorbed by a configuration that represents the death of the system, and there it will remain without incurring cost. Due to the large number of objects, the control problem is studied according to the mean field theory. Thus, instead of analyzing a single object, we focus on the proportions of objects occupying each class, and then we study the limit as
N
goes to infinity. |
| doi_str_mv | 10.1007/s10626-021-00339-z |
| format | Article |
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N
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| subjects | Configurations Control Convex and Discrete Geometry Decision making Discrete time systems Electrical Engineering Machines Manufacturing Mathematics Mathematics and Statistics Mean field theory Operations Research/Decision Theory Processes Stochastic systems Systems Theory Transition probabilities |
| title | A mean field absorbing control model for interacting objects systems |
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