Controlling swarms towards flocks and mills

José A Carrillo (1) , Dante Kalise (2) , Francesco Rossi (3) , Emmanuel Trélat (4, 5)

1 MI - Mathematical Institute [Oxford]
2 Department of Mathematics [Imperial College London]
3 Dipartimento di Matematica [Padova]
4 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
5 CaGE - Control And GEometry

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.

Domaines: Optimisation et contrôle [math.OC]

José A Carrillo, Dante Kalise, Francesco Rossi, Emmanuel Trélat. Controlling swarms towards flocks and mills. 2021. ⟨hal-03167349v2⟩