Formation Control of Multi-agent Systems Over Directed Topologies: A Sliding Mode Control Approach With Prescribed-time Convergence

The advancements in multi-agent systems have gained substantial interest in recent years, particularly their capability of moving in pre-specified formations and carrying out coordinated tasks has garnered significant attention. In this paper, we investigate a comprehensive framework for addressing the formation control problem in multi-agent systems interconnected in directed topologies utilizing a sliding mode control approach. The followers must track a leader using a set of predefined constraints to preserve the needed formation while in motion along the entire path. The sliding mode-based protocol is first formulated for second-order multi-agent systems and then extended to high-order systems. The salient feature of the devised distributed protocol is that it achieves prescribed-time convergence while avoiding the control input singularity as the time approaches a predefined settling time. Finally, the validity and effectiveness of the methodology discussed are demonstrated through simulation examples.