Performance bounds for the mean-field limit of constrained dynamics

TL;DR

This paper establishes a theoretical bound on the difference in cost functionals between model predictive control and optimal control in the mean-field limit of constrained kinetic models, extending previous ODE results.

Contribution

It provides a computable, provable bound on control performance difference in the mean-field limit, linking MPC and optimal control theoretically.

Findings

Derived a bound on the cost functional difference between MPC and optimal control

Extended previous ODE results to mean-field kinetic models

Validated theoretical results with numerical simulations

Abstract

In this work we are interested in the mean-field formulation of kinetic models under control actions where the control is formulated through a model predictive control strategy (MPC) with varying horizon. The relation between the (usually hard to compute) optimal control and the MPC approach is investigated theoretically in the mean-field limit. We establish a computable and provable bound on the difference in the cost functional for MPC controlled and optimal controlled system dynamics in the mean-field limit. The result of the present work extends previous findings for systems of ordinary differential equations. Numerical results in the mean-field setting are given.