A Boltzmann approach to mean-field sparse feedback control

TL;DR

This paper introduces a Boltzmann-based method for designing sparse, optimal feedback controls in large-scale multi-agent systems, addressing high-dimensional challenges through sampling techniques.

Contribution

It proposes a novel Boltzmann approach to synthesize sparse optimal controls for large multi-agent systems, overcoming dimensionality issues.

Findings

Effective sparse control signals generated for kinetic limits

Sampling of two-agent solutions approximates large-scale control

Numerical experiments validate the proposed method

Abstract

We study the synthesis of optimal control policies for large-scale multi-agent systems. The optimal control design induces a parsimonious control intervention by means of l-1, sparsity-promoting control penalizations. We study instantaneous and infinite horizon sparse optimal feedback controllers. In order to circumvent the dimensionality issues associated to the control of large-scale agent-based models, we follow a Boltzmann approach. We generate (sub)optimal controls signals for the kinetic limit of the multi-agent dynamics, by sampling of the optimal solution of the associated two-agent dynamics. Numerical experiments assess the performance of the proposed sparse design.