Prescribed-Time Formation Control for Multi-Agent Systems with Uncertain Nonlinear Dynamics and Non-Vanishing Random Disturbances

This paper investigates the problem of prescribed-time formation control for multi-agent systems with directed communication topology, uncertain nonlinear dynamics, and non-vanishing random disturbances. To drive the formation error to zero within a prescribed time, a novel prescribed-time control lemma is developed. A distributed observer is designed to allow each follower to accurately estimate the leader's states within the prescribed time. Building on this, an observer-based prescribed-time formation control algorithm is proposed. The algorithm ensures that a disordered group of autonomous agents achieves the desired formation with zero error within the prescribed time, despite the presence of uncertain nonlinear dynamics and non-vanishing random disturbances. The prescribed time is arbitrarily predetermined a priori and independent of the agents' initial configurations and any other control parameters. Mathematically, the stability of the proposed control scheme is rigorously proven, where all observer and closed-loop system signals are bounded. Numerical simulations confirm the effectiveness of the proposed formation scheme.