Uncertainty Quantification in Control Problems for Flocking Models

TL;DR

This paper investigates how uncertainty in interaction parameters affects flocking models, using generalized polynomial chaos and model predictive control to analyze and steer the system despite randomness and instability.

Contribution

It introduces a numerical approach combining gPC and model predictive control to manage uncertainty in flocking models, demonstrating effectiveness in unstable regimes.

Findings

Threshold effects in alignment dynamics due to randomness

gPC effectively quantifies uncertainty impacts

Model predictive control successfully steers flocking systems

Abstract

In this paper the optimal control of flocking models with random inputs is investigated from a numerical point of view. The effect of uncertainty in the interaction parameters is studied for a Cucker-Smale type model using a generalized polynomial chaos (gPC) approach. Numerical evidence of threshold effects in the alignment dynamic due to the random parameters is given. The use of a selective model predictive control permits to steer the system towards the desired state even in unstable regimes.