To address the search-and-docking problem in multi-stage prescribed performance switching (MPPS) scenarios, this paper presents a novel compound control method for three-dimensional (3D) underwater trajectory tracking control of unmanned underwater vehicles (UUVs) subjected to unknown disturbances. The proposed control framework can be divided into two parts: kinematics control and dynamics control. In the kinematics control loop, a novel parallel model predictive control (PMPC) law is proposed, which is composed of a soft-constrained model predictive controller (SMPC) and hard-constrained model predictive controller (HMPC), and utilizes a weight allocator to enable switching between soft and hard constraints based on task goals, thus achieving global optimal control in MPPS scenarios. In the dynamics control loop, a finite-time terminal sliding mode control (FTTSMC) method combining a finite-time radial basis function neural network adaptive disturbance observer (RBFNN-FTTSMC) is proposed to achieve disturbance estimation and fast convergence of velocity tracking errors. The simulation results demonstrate that the proposed PMPC-FTTSMC approach achieved an average improvement of 33% and 80% in the number of iterations compared with MPC with sliding mode control (MPC-SMC) and traditional MPC methods, respectively. Furthermore, the approach improved the speed of response by 35% and 44%, respectively, while accurately achieving disturbance observation and enhancing the system robustness.

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