Decentralised minimal-time consensus

in The proceedings of the 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) (2011)

This study considers the discrete-time dynamics of a network of agents that exchange information according to the nearest-neighbour protocol under which all agents are guaranteed to reach consensus ... [more ▼]

This study considers the discrete-time dynamics of a network of agents that exchange information according to the nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically. We present a fully decentralised algorithm that allows any agent to compute the consensus value of the whole network in finite time using only the minimal number of successive values of its own history. We show that this minimal number of steps is related to a Jordan block decomposition of the network dynamics and present an algorithm to obtain the minimal number of steps in question by checking a rank condition on a Hankel matrix of the local observations. Furthermore, we prove that the minimal number of steps is related to other algebraic and graph theoretical notions that can be directly computed from the Laplacian matrix of the graph and from the underlying graph topology. [less ▲]

Decentralized final value theorem for discrete-time LTI systems with application to minimal time distributed consensus

in The proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (2009)

In this study, we consider an unknown discrete-time, linear time-invariant, autonomous system and characterise, the minimal number of discrete-time steps necessary to compute the asymptotic final value of ... [more ▼]

In this study, we consider an unknown discrete-time, linear time-invariant, autonomous system and characterise, the minimal number of discrete-time steps necessary to compute the asymptotic final value of a state. The results presented in this paper have a direct link with the celebrated final value theorem. We apply these results to the design of an algorithm for minimal-time distributed consensus and illustrate the results on an example. [less ▲]