Specified-time containment control of multi-agent systems over directed topologies

This study addresses the specified-time containment control problem of multi-agent systems over directed topologies. By using motion-planning approaches, a new framework is constructed to solve the containment control problem of multi-agent systems. In this framework, a class of sampled-data-based protocols are proposed to solve the specified-time containment control problem for single-integrator multi-agent systems. These protocols only require relative information measurements at the sampling instants, without requiring information exchange over the sampling interval. Furthermore, the containment protocols are also developed for the multi-agent system with double-integrator dynamics, such that their states converge to the convex hulls formed by those of the target points in a specified settling time over directed topologies. Compared with the existing results, the proposed sampled-data-based protocols have a couple of advantages: first the settling time can be pre-specified, which is very meaningful and consistent with practical needs. Second, the sampling periods, communication topologies and control gains are all decoupled and can be separately designed. This relaxes many restrictions in controllers design. Numerical simulations are provided to demonstrate the effectiveness of the proposed protocols.