Specified-time containment tracking for multi-agent systems: An optimal control approach

In this paper, for single-integrator multi-agent systems, specified-time containment tracking problem is studied under undirected topologies. By utilizing specified-time optimal control approaches, a class of novel containment tracking algorithms are proposed. In order to solve the containment control problem in a settling time specified in advance, a sampling time sequence, which converges to the specified time, is designed. During each time interval of the sampling time sequence, the proposed algorithm is used for single-integrator multi-agent systems. Thus, the proposed algorithm is a sampling-data-based specified-time containment tracking algorithm. Due to the settling time can be specified in advance, this algorithm is very meaningful and consistent with practical requirements. Finally, we propose a numerical simulation to show the effectiveness of the theoretical results.