Combinatorial Admissibility in Control-Affine Networks

TL;DR

This paper investigates the conditions under which heterogeneous control-affine nonlinear agents can synchronize through diffusive measurements, introducing combinatorial certificates linking graph topology and actuation limits.

Contribution

It introduces an admissibility concept and practical combinatorial certificates to verify feasible edge-driven diffusive designs for synchronization.

Findings

Derived checkable certificates connecting graph topology and actuation limits to admissibility

Established a framework for verifying synchronization feasibility in control-affine networks

Illustrated results on nonlinear oscillator synchronization

Abstract

We study synchronization of heterogeneous control-affine nonlinear agents interconnected through diffusive (relative-output) measurements. We separate the design into an edge-space step, specifying a stabilizing model evolution for relative outputs, and a lift step, realizing the prescribed edge motion using the agents' allowable input directions, constrained by the control-affine geometry of the agents. We introduce an admissibility notion that characterizes when an edge-driven diffusive design is feasible. We derive checkable combinatorial certificates that connect graph topology and actuation limits directly to admissibility, so that feasible edge dynamics can be verified in a practical and transparent way. The results are illustrated on synchronization of nonlinear oscillators.