Optimal Scheduling of Downlink Communication for a Multi-Agent System with a Central Observation Post

In this letter, we consider a set of agents, which may receive an observation of their state by a central observation post via a shared wireless network. The aim of this letter is to design a scheduling mechanism for the central observation post to decide how to allocate the available communication resources. The problem is tackled in two phases: first, the local controllers are designed so as to stabilize the subsystems for the case of perfect communication and second, the communication schedule is decided with the aim of maximizing the stability of the subsystems. To this end, we formulate an optimization problem which explicitly minimizes the Lyapunov function increase due to communication limitations. We show how the proposed optimization can be expressed in terms of value of information, we prove Lyapunov stability in probability and we test our approach in simulations.