Finite-Time Distributed Protocol for Tracking the Upper (Lower) Bound For a Set of Time-Varying Reference Signals

In this paper we address the problem of distributively tracking the upper or lower bound of n time-varying signals in finite-time. In detail, each agent has access to a time-varying exogenous signal, which may encode the evolution of a physical phenomenon. All the agents are required to follow the upper (lower) bound value among such output signals in a distributed fashion. We provide a protocol to solve the above problem in the case of networked agents and undirected communication, together with formal proof of convergence and estimation of an upperbound of the convergence time. We corroborate the protocol via numerical validations in a precision farming setting.