Max-Consensus Over Fading Wireless Channels

This paper deals with the problem of achieving finite-time max-consensus in a multi-agent system that communicates over a fading wireless channel. A key feature of the wireless channel is the superposition (or broadcast) property. In traditional wireless communication systems, the superposition property is usually undesired since it might cause interference that drastically degrades system performance. In contrast, in the multi-agent system considered in this paper, different agents aim at achieving max-consensus. Therefore, rather than combatting interference due to the superposition property, we design a communication system that exploits this property for a more efficient usage of wireless resources. By simultaneously accessing the wireless channel, each agent obtains a weighted average of the neighboring agents' information states, where weights (namely, channel coefficients) are unknown and fading. Given that each agent has access to this piece of information, we present a switching consensus protocol employing broadcast autorisations for agents and show that max-consensus can be achieved under this protocol within a finite number of iterations.