Prescribed-time distributed control with Periodic Time Transformation

This paper presents a control design framework for Multi-Agent System (MAS) to address Leader–Follower (L–F) consensus and tracking problems. First, for the uncertainty-free system, a general control framework is proposed, which ensures that the system can stabilize at a user-defined time (denoted as T) and maintain stability after time T. Then, a Periodic Time Transformation Function (PTTF) approach is proposed, which can incorporate both vanishing and non-vanishing uncertainties into the prescribed-time control design. A distributed control algorithm based on PTTF is presented, enabling followers to converge to the leader at time T, periodically track the leader after time T, and suppress uncertainties throughout the entire time axis. It is demonstrated that the control signals are bounded.