Convergence Analysis of Classes of Asymmetric Networks of Cucker–Smale Type With Deterministic Perturbations

Abstract

We discuss two extensions of the Cucker-Smale flocking model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence of identical internal dynamics. The second model describes a similar population of agents that perform velocity alignment with the restriction of collision-free orbits. Although qualitatively different, we explain how these models can be analyzed under a common framework. Rigorous analysis is conducted toward establishing sufficient conditions for asymptotic flocking to a synchronized motion. Applications of our results are compared with simulations to illustrate the effectiveness of our theoretical estimates.