Data-driven control of consensus tracking for discrete-time multi-agent systems

This paper investigates the consensus tracking problem of leader-follower multi-agent systems. Different from most existing works, dynamics of all the agents are assumed completely unknown, whereas some input-output data about the agents are available. It is well known from the Willems et al. Fundamental Lemma that when inputs of a linear time-invariant (LTI) system are persistently exciting, all possible trajectories of the system can be represented in terms of a finite set of measured input-output data. Building on this idea, the present paper proposes a purely data-driven distributed consensus control policy which allows all the follower agents to track the leader agent's trajectory. It is shown that for a linear discrete-time multi-agent system, the corresponding controller can be designed to ensure the global synchronization with local data. Even if the data are corrupted by noises, the proposed approach is still applicable under certain conditions. Numerical examples corroborate the practical merits of the theoretical results.