Distributed computation of minimum time consensus for multi-agent systems

The problem of computing the minimum time to consensus of multiple identical double-integrator agents is considered. A distributed algorithm for computing the final consensus target state is proposed. Local feedback time optimal control laws are synthesized to drive each agent to the computed final consensus target state. Each agent is assumed to know the states of every other agent. As a part of the algorithm, every possible triplet of agents compute their mutual minimum time to consensus. The maximum value among these triplet minimum times is shown to be the required minimum time to consensus for the entire group. Since the required computation can be performed for each triple separately, it can be distributed evenly among the agents.