Robust sparse formation tracking control for multiple autonomous underwater vehicle systems under severe hybrid stochastic delays

Formation trajectory tracking for multiple autonomous underwater vehicles (AUVs) is challenged by hybrid stochastic delays and lumped disturbances arising from hydrodynamic uncertainties and ocean currents. These problems are exacerbated in sparse formation scenarios, where the large inter-AUV distances are required for wide-area missions. To overcome these challenges, a novel trend-guided Gaussian process regression (TG-GPR) enhanced dual-loop distributed sliding mode tube-based model predictive control (DSMT-MPC) framework is proposed in this paper for sparse formation tracking of multi-AUV systems. Specifically, the TG-GPR algorithm is developed to compensate for severe hybrid stochastic delays of up to ten seconds and to predict neighbor states under non-stationary error dynamics. Concurrently, an adaptive radial basis function neural network observer estimates intense lumped disturbances in real time. The dual-loop DSMT-MPC architecture guarantees constraint satisfaction and optimizes the controller input. A logistic growth function is designed to replace the sign function in the auxiliary controller to suppress chattering and confine states within an invariant tube. The recursive feasibility and uniformly ultimately bounded closed-loop practical stability of the controller are substantiated. Finally, simulation results validate the effectiveness and superiority of the TG-GPR enhanced dual-loop DSMT-MPC framework. Crucially, compared with the strongest baseline, the proposed method reduces the position tracking root-mean-squared error and the constraint violation ratio by 56.2% and 81.6%, respectively. Consequently, the present study provides a theoretical basis for the practical engineering application of AUVs in wide-area maritime missions.