Predefined-Time Formation Control of NMSVs With External Disturbance via Vector Control Lyapunov Functions-Based Method

This article investigates the problem of predefined-time distributed formation tracking for networked marine surface vehicles in the presence of external disturbances. To address this problem, we propose a novel hierarchical predefined-time formation control (HPTFC) framework that integrates a novel sliding mode surface with the vector control Lyapunov functions-based (VCLFs) method. Specifically, the local control layer based on VCLFs is established, which circumvents the usual requirement for positive-definite Lyapunov functions and only necessitates semidefinite positive components. This enables us to search for more appropriate control algorithms in a broader solution space generated by more suitable Lyapunov functions with more general conditions. Through comprehensive theoretical analysis, we demonstrate that the proposed HPTFC framework achieves predefined-time convergence successfully. Eventually, numerical simulations are exhibited to illustrate the effectiveness and superiority of the proposed HPTFC scheme.