Specified-Time Formation-Containment Control for General Linear Multi-Agent Systems Over Layered Interaction Networks

This paper addresses the specified-time formation-containment control problem for general linear multi-agent systems over directed interaction networks. The interaction network is divided into three layers containing a tracking-leader with a bounded input, formation-leaders and followers. First, under overall planning and multi-step control framework, a novel terminal constraint is designed. Then, by applying Pontryagin’s maximum principle, a class of distributed specified-time formation-containment control algorithms is developed, where the settling time can be pre-specified and independent of system parameters or initial states. Further, robustness analysis against bounded unknown disturbances is rigorously conducted to validate disturbance rejection capabilities. Finally, a simulation example involving multi-robot formation-containment control is presented to demonstrate the effectiveness of the proposed algorithms.