## Abstract

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.

Original language | English |
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Pages (from-to) | 349-372 |

Number of pages | 24 |

Journal | Discrete Event Dynamic Systems: Theory and Applications |

Volume | 31 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2021 |

### Bibliographical note

Funding Information:Work partially supported by Consejo Nacional de Ciencia y Tecnología (CONACYT-México) under grant Ciencia Frontera 87787.

Publisher Copyright:

© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.

## Keywords

- Control problems
- Mean field theory
- Optimal policies
- Random horizon
- Systems of interacting objects