Time-varying formation tracking for multi-agent systems based on prescribed-time control

In this paper, a time-varying formation tracking method based on prescribed-time control is presented for second-order multi-agent systems. The control objective is that the formation system forms and maintains the desired time-varying configuration within an arbitrarily specified time. Addressing the problem that the existing prescribed-time control theorem may lead to divergence of system caused by infinite control input, a novel prescribed-time control theorem based on a novel time-varying scale function is proposed. Different from the existing prescribed-time control results, the proposed theorem introduces convergence time, lead time and prescribed time to avoid the occurrence of the infinite control input. Meanwhile, it can estimate the actual convergence time and has faster convergence rate. Based on proposed theorem, a distributed prescribed-time observer is designed to estimate leader’s states for each follower (suppose that only a few followers can obtain the states of leader) and a prescribed-time formation tracking controller is designed with the estimations of the observer to track leader. Both the observer and controller achieve the prescribed-time stability. Finally, a simulation example is proposed to verify the efficiency of the main results.