A distributed protocol for finite-time supremum or infimum dynamic consensus: The directed graph case

This paper proposes a distributed protocol for tracking the global maximum supremum (or minimum infimum) of a set of exogenous time-varying signals. Specifically, each agent has only access to one of these signals and, by implementing the proposed protocol, it is able to track in finite-time the maximum supremum (or the minimum infimum) of the exogenous time-varying signals in a distributed fashion. No assumption is made on the network size and, remarkably, the communication graph is directed (possibly switching) with the only requirement to be strongly connected at all times. The behavior of the protocol with open networks is discussed and numerical simulations are provided to corroborate the theoretical findings.