Fast distributed output synchronisation of heterogeneous multi-agent systems: a perfect zero-sum game

Most recent works on optimal synchronisation of multi-agent systems have overlooked the impact of settling time on whole performance and cannot achieve a fast response. This paper proposes a novel optimal distributed control protocol that realises the arbitrarily fast output synchronisation of linear heterogeneous multi-agent systems over an acyclic communication graph. By Cayley–Hamilton extended theorem, we introduce an auxiliary system to formulate the cooperative output tracking problem as a perfect zero-sum game. The necessary and sufficient conditions are derived for the existence of minmax strategy to this problem. We prove that, under routine assumptions, the obtained optimal distributed protocol has the ability to drive each follower's output to follow the leader's output trajectory with arbitrarily small settling time, under any initial conditions. Also, the robustness property of each follower's control from minmax strategy is determined. Finally, our theoretical results are verified by a simulation example.