Reaching consensus at a preset time: Single-integrator dynamics case

In the paper, a novel finite-time consensus framework for multi-agent systems with single-integrator dynamics is established. In such a framework, the multi-agent team can achieve consensus at any preset time. In order to reach this goal, linear feedback control protocols with time-varying gains are introduced. For both undirected and directed communication networks, specific functions for time-varying gains are considered and then the results in general form are derived, respectively. The proposed preset time dependent time-varying control protocols can solve consensus problems at the preset time if the undirected communication topology is connected or the directed communication topology has a spanning tree. Numerical simulations are presented to illustrate the effectiveness of the obtained theoretical results.