Stability properties of a receding horizon controller for cooperating UAVs

We consider a setting where multiple vehicles form a networked team cooperating to visit multiple target points associated with rewards. The goal is to maximize the total reward accumulated over a given time interval. We have proposed a receding horizon (RH) control scheme which dynamically determines vehicle trajectories by solving a sequence of optimization problems over a planning horizon and executing them over a shorter action horizon. A key property observed in the operation of this scheme is that the trajectories are stationary, in the sense that they ultimately assign vehicles to target points, even though the controller is not explicitly designed to perform such discrete point assignments. In prior work, conditions under which this property is guaranteed were obtained for the 1-vehicle, N-target point case. In this paper, we extend this analysis to 2-vehicle cases, despite the resulting loss of convexity.