Predefined-Time Distributed Time-Varying Optimal Formation Control for Networked Marine Surface Vehicles Under Disturbances

This paper investigates the predefined-time distributed optimal formation control problem for networked marine surface vehicles (NMSVs) with time-varying optimization objectives and external disturbances. The objective is to drive all vehicles to track the time-varying global optimal trajectory generated by the distributed estimator while maintaining prescribed formation within a predefined time. Accordingly, a hierarchical optimization–formation control framework is developed to bridge global trajectory optimization and local formation control. In the optimization layer, a predefined-time distributed optimization estimator is developed based on local time-varying cost information and neighboring information exchange, which is employed to generate the optimal reference signal. The optimal reference signal is then embedded into the formation control layer, where a tracking controller with a predefined-time segmented terminal sliding-mode surface is designed to compensate for ocean disturbances and ensure accurate trajectory tracking. Lyapunov analysis proves that both the optimization estimation errors and the formation tracking errors converge to zero within a predefined time. Simulation results, including quantitative comparisons, fleets of up to 40 NMSVs, switching and jointly connected graphs, communication impairments, heterogeneous time-varying costs, and rapid references, demonstrate the convergence accuracy, scalability, and practical limits of deadline preservation.