Abstract: This disclosure relates to distributed control of a platoon of vehicles with nonlinear dynamics. Distributed receding horizon control algorithms are presented to derive sufficient conditions that guarantee asymptotic stability, leader-follower string stability, and predecessor-follower string stability, following a step speed change in the platoon. Vehicles compute their own control in parallel, and receive communicated position and velocity error trajectories from their immediate predecessor. Leader-follower string stability requires additional communication from the lead car at each update, in the form of a position error trajectory. Communication from the lead car is required only once at initialization. Provided an initially feasible solution can be found, subsequent feasibility of the algorithms are guaranteed at every update. The theory is generalized for nonlinear decoupled dynamics, and is thus applicable to fleets of planes, robots, or boats, in addition to cars.