The turnpike property for high‐dimensional interacting agent systems in discrete time

Optimal Control Applications and Methods, vol. 45, pp. 2557–2571

Abstract

Abstract We investigate the interior turnpike phenomenon for discrete‐time multi‐agent optimal control problems. While for continuous systems the turnpike property has been established, we focus here on first‐order discretizations of such systems. It is shown that the resulting time‐discrete system inherits the turnpike property with estimates of the same type as in the continuous case. In particular, we prove that the discrete time optimal control problem is strictly dissipative and the cheap control assumption holds.

Authors 4

1. Martin Gugat

   Friedrich-Alexander-Universität Erlangen-Nürnberg

   Affiliation as printed

   Chair in Dynamics, Control, Machine Learning and Numerics‐Alexander von Humboldt Professorship Friedrich‐Alexander Universität Erlangen‐Nürnberg (FAU) Erlangen Germany

2. Michaël Herty Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik RWTH Aachen University Aachen Germany

3. Jiehong Liu

   Sapienza University of Rome

   Affiliation as printed

   Department of Mathematics Guido Castelnuovo Sapienza University of Rome Roma Italy

   Department of Mathematics Guido Castelnuovo, Sapienza University of Rome, Roma, Italy

4. Chiara Segala corresponding Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik RWTH Aachen University Aachen Germany