Moment-Driven Predictive Control of Mean-Field Collective Dynamics

TL;DR

This paper develops a moment-driven predictive control framework for mean-field collective dynamics, combining linearization, Riccati equations, and adaptive nonlinear model predictive control to improve performance and robustness.

Contribution

It introduces a novel control approach that integrates linearization-based feedback with adaptive model predictive control for mean-field systems.

Findings

Effective control laws derived from Riccati equations

Enhanced robustness demonstrated through numerical experiments

Adaptive control improves performance in collective dynamics

Abstract

The synthesis of control laws for interacting agent-based dynamics and their mean-field limit is studied. A linearization-based approach is used for the computation of sub-optimal feedback laws obtained from the solution of differential matrix Riccati equations. Quantification of dynamic performance of such control laws leads to theoretical estimates on suitable linearization points of the nonlinear dynamics. Subsequently, the feedback laws are embedded into nonlinear model predictive control framework where the control is updated adaptively in time according to dynamic information on moments of linear mean-field dynamics. The performance and robustness of the proposed methodology is assessed through different numerical experiments in collective dynamics.