Advection on Graphs
Consensus is a popular linear protocol for the network dynamics. Consequently, it is a rich area of research. We explore the advection protocol which shares many characteristics of consensus, facilitating the extension of many of the consensus results to advection. The advection protocol proves advantageous to formation control and load balancing applications. We demonstrate the latter with our robotic platform.
Linear consensus can also be generalized to nonlinear consensus. The Laplacian matrix, the system matrix at the heart of consensus, lives in the family of Z-matrices. Many results from nonlinear consensus generalize to nonlinear Z-matrix applications. We explore these results, which include the characterization of the set of equilibria and the establishment of asymptotic stability