Exponential turnpike property for particle systems and mean-field limit

TL;DR

This paper proves exponential turnpike properties for optimal control problems involving particle systems and their mean-field limits, demonstrating that these properties persist as the number of particles approaches infinity.

Contribution

It establishes exponential estimates for optimal states and controls under strict dissipativity and shows these results hold in the mean-field limit.

Findings

Exponential estimates for optimal states and controls are proven.

Results for particle systems are preserved in the mean-field limit.

The exponential turnpike property holds under strict dissipativity.

Abstract

This work is concerned with the exponential turnpike property for optimal control problems of particle systems and their mean-field limit. Under the assumption of the strict dissipativity of the cost function, exponential estimates for both optimal states and optimal control are proven. Moreover, we show that all the results for particle systems can be preserved under the limit in the case of infinitely many particles.