Stability properties of a cooperative Receding Horizon controller

We consider a setting where multiple vehicles form a team cooperating to visit multiple target points to collect rewards associated with them. The team objective is to maximize the total reward accumulated over a given time interval. Complicating factors include uncertainties regarding the locations of target points and the effectiveness of collecting rewards, differences among vehicle capabilities, and the fact that rewards are time-varying. 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. This paper makes use of the potential field method and establishes conditions under which this property holds and fully studies settings which are analytically tractable.