Set-Consensus using Set-Valued Observers

This paper addresses the problem of reaching consensus when the position measurements are corrupted by noise and taken at different time instants. Two different scenarios are considered, namely: when the sensor function is performed on a group of nodes and sent to those nodes at the same time; and a second case where the transmission is unicast but neighboring nodes receive the message due to the shared nature of the wireless medium. A solution involving Set-Valued Observers (SVOs) is proposed to maintain and update the set-valued estimates for the positions and how to drive the agents. The algorithm is proved to enforce convergence of the nodes to clusters up to a factor dependent on the uncertainty. The performance of the proposed algorithm is assessed through simulations, illustrating, in particular how the choice for selecting how to divide the area can reduce or increase the number of clusters.