**4. Methodology**

In order to address the external ocean current disturbance and parametric uncertainties of the Coriolis and centripetal matrix and the hydrodynamic damping matrix, a tube-based event-triggered path-tracking strategy consisting of a LMPC controller and a tube MPC controller is developed. The scheme of the proposed path-tracking strategy is shown in Figure 2.

**Figure 2.** Scheme of the proposed path-tracking strategy.

Based on the kinematics model, the LMPC controller is used to address Problem 1, whose inputs are the reference waypoint and real-time nominal states of the AUV, and outputs are the speed control law.

Based on decoupled models (19), (20), and (22), according to the speed control law and real-time states of the AUV, the tube MPC controller is used to compute optimal control inputs of the AUV. The nominal control law is obtained by solving a constrained optimal control problem. According to these decoupled models, the surge speed will have a great effect on the AUV's state, and the mismatch of these decoupled models may depend on the surge speed. These offline calculated invariable constraints on the nominal system may be too conservative. According to the change in the surge speed command, an event-triggering strategy is used to formulate an adaptive flexible tube to deal with the mismatch.
