Advection on graphs

This paper examines the dynamics of a networked, multi-agent system operating with an advection-based coordination algorithm. Flow advection is a close relative of diffusion whose discretized version forms the basis of the popular consensus dynamics. We endeavor to demonstrate in this paper that discretizing the continuous advection equation also forms an attractive set of system dynamics for coordinated control. The key advantage of advection-based algorithms over directed consensus is that the sum of the states is always conserved. This paper includes a formulation of the advection dynamics on directed graphs and a presentation of some of its characteristics, which are compared to the consensus dynamics. We also provide examples of the versatility of the advection dynamics: a formation control and sensor coverage example.