Computation of the target state and feedback controls for time optimal consensus in multi-agent systems

ABSTRACT N identical agents with bounded inputs aim to reach a common target state (consensus) in the minimum possible time. Algorithms for computing this time-optimal consensus point, the control law to be used by each agent, and the time taken for the consensus to occur, are proposed. Two types of multi-agent systems are considered, namely 1) coupled single-integrator agents on a plane and, 2) double-integrator agents on a line. At the initial time instant, each agent is assumed to have access to the state information of all the other agents. An algorithm, using convexity of attainable sets and Helly’s theorem, is proposed, to compute the final consensus target state and the minimum time to achieve this consensus. Further, parts of the computation are parallelized amongst the agents such that each agent has to perform computations of O(N2) run time complexity. Finally, local feedback time optimal control laws are synthesized to drive each agent to the target point in minimum time. During this part of th...