Combinatorial Admissibility in Control-Affine Networks

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.