Edges' Riemannian energy analysis for synchronization of multi-agent nonlinear systems over undirected weighted graphs

Vincent Andrieu (1, 2) , Daniele Astolfi (1, 2) , Alexandre Cellier-Devaux (2)

1 CNRS - Centre National de la Recherche Scientifique
2 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique

In this note we investigate the problem of global exponential synchronization of multi-agent systems described by nonlinear input affine dynamics. We consider the case of networks described by undirected connected graphs possibly without leader. We present a set of sufficient conditions based on a Riemannian metric approach in order to design a state-feedback distributed control law. Then, we study the convergence properties of the overall network. By exploiting the properties of the edge Laplacian we construct a Lyapunov function that allows to conclude global exponential synchronization of the overall network.

Mots clés: Synchronization multi-agent systems edge Laplacian nonlinear systems; Synchronization; multi-agent systems; edge Laplacian; nonlinear systems

Domaines: Optimisation et contrôle [math.OC]

Vincent Andrieu, Daniele Astolfi, Alexandre Cellier-Devaux. Edges' Riemannian energy analysis for synchronization of multi-agent nonlinear systems over undirected weighted graphs. Automatica, inPress, ⟨https://doi.org/10.1016/j.automatica.2024.111950⟩. ⟨hal-04759628⟩