Distributed algebraic connectivity estimation for adaptive event-triggered consensus

Abstract—In several multi agent control problems, the con-vergence properties and speed of the system depend on the algebraic connectivity of the graph. We discuss a particular event-triggered consensus scenario, and show that the availabil-ity of an estimate of the algebraic connectivity could be used for adapting the behavior of the average consensus algorithm. We present a novel distributed algorithm for estimating the al-gebraic connectivity, that relies on the distributed computation of the powers of matrices. We provide proofs of convergence, convergence rate, and upper and lower bounds at each iteration of the estimated algebraic connectivity. I