Finite-Gain Prescribed-Time-Synchronized Formation Control for ASVs Under Output Constraints

This study investigates prescribed-time-synchronized (PTS) formation control for multiple autonomous surface vehicles (ASVs) subject to time-varying output constraints. A novel prescribed-time stability lemma is first established, which provides a general approach for constructing a new class of finite-gain adjustment functions that satisfy specified integral conditions. This approach effectively avoids the high-gain behavior typically caused by unbounded scaling functions in conventional temporal transformations. Based on this result, we develop a PTS constrained stable system (PTSCSS) that ensures simultaneous convergence of all state components to the origin within the prescribed time, with finite gains maintained throughout the time domain. Moreover, the time-varying constraints are strictly satisfied after a designated switching instant for any initial condition. Subsequently, a PTSCSS-based sliding manifold and a finite-gain sliding-mode formation controller are proposed for the ASV formation model. The PTS stability of the closed-loop system is rigorously proved via Lyapunov analysis. Finally, comparative simulations with multiple ASVs validate the effectiveness of the proposed control method.