Many successful control schemes for land-based or air-based groups, or platoons, of autonomous vehicles cannot be implemented in underwater applications because of their dependence upon high-bandwidth communication. In current strategies for controlling groups of autonomous underwater vehicles (AUVs), platoon size remains limited by communication bandwidth requirements. So, there is great need for advances in low-bandwidth control techniques for arbitrarily large platoons of AUVs. This thesis presents a new approach to multiple vehicle control. The concepts described herein enable an arbitrarily large platoon to be controlled while utilizing minimal inter-vehicle communication. Specifically, this thesis examines a sufficient condition on platoon commands in order for a low-bandwidth decentralized controller to exist. Knowing from this sufficient condition the necessary general form of platoon commands, a number of higher-order statistics were tested. This thesis describes and analyzes their utility as platoon commands. In addition to these theoretical developments, this thesis presents the practical design needs for the Virginia Tech miniature autonomous underwater vehicle as well as their resolution. / Master of Science