Controlling swarms towards flocks and mills

TL;DR

This paper develops control methods for second-order swarming systems to reliably steer any initial configuration into flock or mill formations, combining theoretical analysis and computational validation.

Contribution

It introduces a novel control framework using LaSalle invariance, Lyapunov functionals, and linearization techniques to achieve flock and mill stabilization in swarms.

Findings

Control can steer any initial swarm to flock or mill formations.

The proposed feedback laws are theoretically validated and computationally tested.

Stability analysis guides effective control law design.

Abstract

Self-organization and control around flocks and mills is studied for second-order swarming systems involving self-propulsion and potential terms. It is shown that through the action of constrained control, is it possible to control any initial configuration to a flock or a mill. The proof builds on an appropriate combination of several arguments: LaSalle invariance principle and Lyapunov-like decreasing functionals, control linearization techniques, and quasi-static deformations. A stability analysis of the second-order system guides the design of feedback laws for the stabilization to flock and mills, which are also assessed computationally.