The turnpike property for mean-field optimal control problems

arXiv (Cornell University)

Abstract

We study the turnpike phenomenon for optimal control problems with mean field dynamics that are obtained as the limit $N\rightarrow \infty$ of systems governed by a large number $N$ of ordinary differential equations. We show that the optimal control problems with with large time horizons give rise to a turnpike structure of the optimal state and the optimal control. For the proof, we use the fact that the turnpike structure for the problems on the level of ordinary differential equations is preserved under the corresponding mean-field limit.

Authors 3

1. Martin Gugat

   Friedrich-Alexander-Universität Erlangen-Nürnberg

   Affiliation as printed

   Chair in Dynamics, Control and Numerics (Alexander von Humboldt-Professorship),

   Department of Data Science, Friedrich-Alexander Universität Erlangen-Nürnberg (FAU), Cauerstr. 11, 91058 Erlangen, Germany,

2. Michaël Herty Aachen Chair in Numerical Analysis

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

   Chair in Numerical Analysis, IGPM, RWTH Aachen University, Templergraben, 55, D-52062 Aachen, Germany

3. Chiara Segala Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

   IGPM, RWTH Aachen University, Templergraben, 55, D-52062 Aachen, Germany