The turnpike property for mean-field optimal control problems

European Journal of Applied Mathematics, vol. 35, pp. 733–747

Abstract

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 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

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

2. Michaël Herty Aachen

   RWTH Aachen University

   Affiliation as printed

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

3. Chiara Segala corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

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