Saturated Precise Robust Singular Spectrum Analysis-Diffusion Model Predictive Control of AUVs

Accurate path following by autonomous underwater vehicles (AUVs) in wave-dominated environments is limited by two coupled engineering constraints: feedback-driven disturbance observers (DOBs) exhibit phase lag, whereas aggressive cancellation of high-frequency components can exceed the vehicle and actuator bandwidths. This article develops a closed-loop predictive compensation architecture, termed singular spectrum analysis-diffusion (S²D)-model predictive control (MPC) that integrates a S²D observer, a dynamics-informed adaptive filter (DIAF), and MPC. The observer combines instantaneous Kalman-filter (KF) estimates, singular spectrum analysis (SSA)-based trend-residual decomposition, and conditional skip-step diffusion to forecast the disturbance sequence over the MPC horizon. The DIAF then applies saturation and bandwidth-aware filtering so that only physically actionable components enter the feedforward channel. This perception-prediction-decision-action loop retains constraint handling while converting delayed disturbance estimates into phase-leading compensation. Regional input-to-state practical stability (RISPS) is established for the resulting closed loop. Under JONSWAP wave disturbances, the proposed method yields the lowest integrated absolute error (2.09 m $\cdot $ s), an average execution time of 33.25 ms for a 50-ms sampling interval, and integral absolute error (IAE) values of 2.054-2.136 across the tested sea states.