Journal
APPLIED MATHEMATICS AND OPTIMIZATION
Volume 85, Issue 2, Pages -Publisher
SPRINGER
DOI: 10.1007/s00245-022-09837-4
Keywords
Mean-field optimal control; Selective control; Population dynamics; Leader-follower dynamics; Gamma-Convergence; Superposition principle
Categories
Funding
- FWF [OeAD-WTZ CZ 01/2021, I 5149]
- Starting grant per giovani ricercatori of Politecnico di Torino
- Italian Ministry of Education, University
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This paper studies a mean-field selective optimal control problem of multipopulation dynamics via transient leadership. The problem considers the spatial position and probability of belonging to a certain population for the agents, and introduces an activation function to tune the control on each agent. By using Gamma-convergence, the mean-field limit of the finite-particle control problem is identified, ensuring the convergence of optimal controls. Specific applications in the context of opinion dynamics are discussed.
A mean-rield selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population. The dynamics in the control problem is characterized by the presence of an activation function which tunes the control on each agent according to the membership to a population, which, in turn, evolves according to a Markov-type jump process. In this way, a hypothetical policy maker can select a restricted pool of agents to act upon based, for instance, on their time-dependent influence on the rest of the population. A finite-particle control problem is studied and its mean-field limit is identified via Gamma-convergence, ensuring convergence of optimal controls. The dynamics of the mean-field optimal control is governed by a continuity-type equation without diffusion. Specific applications in the context of opinion dynamics are discussed with some numerical experiments.
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