Expander Families as Information Patterns for Distributed Control of Vehicle Platoons

A state space formulation of the distributed control of a 1-D vehicle platoon is considered. The objective is to understand the effects of the underlying information exchange pattern between the vehicles on the control performance of the platoon. The symmetric control case is considered where each vehicle gives equal weight to all the information available to it in determining its control law. It is shown that expander families of graphs when used as information patterns result in stability margins decaying to zero at rate at most O(1/N); an improvement over the previously known O(1/N^2) decay with nearest neighbor type information patterns.