Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $1$-dimensional multi-agent optimal control with aggregation and
  distance constraints: qualitative properties and mean-field limit   In this paper we consider an optimal control problem for a large population
of interacting agents with deterministic dynamics, aggregating potential and
constraints on reciprocal distances, in dimension 1. We study existence and
qualitative properties of periodic in time optimal trajectories of the finite
agents optimal control problem, with particular interest on the compactness of
the solutions' support and on the saturation of the distance constraint.
Moreover, we prove, through a $\Gamma$-convergence result, the consistency of
the mean-field optimal control problem with density constraints with the
corresponding underlying finite agent one and we deduce some qualitative
results for the time periodic equilibria of the limit problem.

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The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph