Multi-agent control in degraded communication environments

The goal of this paper is to compute transmission rates and delays that provably stabilize Multi-Agent Systems (MASs) in the presence of disturbances and noise. In other words, given the existing information delay among the agents and the underlying communication topology, we determine rates at which information between the agents need to be exchanged such that the MAS of interest is ℒ_p-stable with bias, where this bias accounts for distorted/noisy data. In an effort to consider MASs characterized by sets of equilibrium points, the notions of ℒ_p-stability (with bias) and ℒ_p-detectability with respect to a set are utilized. Using Lyapunov-Razumikhin type of arguments, we are able to consider delays that are greater than the transmission intervals. The present methodology is applicable to general (not merely to single- and double-integrator) heterogeneous linear agents, directed topologies and output feedback. The computed transmission rates are experimentally verified employing a group of off-the-shelf quadcopters.