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arXiv · 2205.08921

Optimal control problems of nonlocal interaction equations

S. Fagioli·A. Kaufmann·E. Radici
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Abstract

In the present work we deal with the existence of solutions for optimal control problems associated to transport equations. The behaviour of a population of individuals will be influenced by the presence of a population of control agents whose role is to lead the dynamics of the individuals towards a specific goal. The dynamics of the population of individuals is described by a suitable nonlocal transport equation, while the role of the population of agents is designed by the optimal control problem. This model has been first studied in [12] for a class of continuous nonlocal potentials, while in the present project we consider the case of mildly singular potentials in a gradient flow formulation of the target transport equation.

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S. Fagioli, A. Kaufmann, E. Radici. 2022-05-18. Optimal control problems of nonlocal interaction equations. https://arxiv.org/abs/2205.08921

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