An Adaptive Distributed Protocol for Finite-time Infimum or Supremum Dynamic Consensus

In this paper, the problem of distributively tracking the minimum infimum (or maximum supremum) of a set of time-varying signals in finite-time is addressed. More specifically, each agent has access to a local time-varying exogenous signal, and all the agents are required to follow the minimum infimum (or the maximum supremum) of these signals in a distributed fashion. No assumption is made on the network size nor on the bounds of the exogenous signal derivatives. An adaptive protocol is provided which can provably solve the above problem in finite-time for multi-agent systems with undirected connected network topologies. Numerical simulations are provided to corroborate the theoretical findings.