Tube-based deep Koopman model predictive control for planar trajectory tracking of autonomous underwater vehicles

Trajectory tracking of autonomous underwater vehicles (AUVs) is challenging in the presence of model uncertainty, external disturbances, and limited onboard computational resources. Model predictive control (MPC) is a promising approach for AUV trajectory tracking, but the nonlinear dynamics of AUVs and their limited onboard computational resources make its real-time implementation challenging. To address this issue, this paper proposes a tube-based deep Koopman model predictive control framework for trajectory tracking of AUVs. A deep neural network is employed to learn lifting functions from data and construct a finite-dimensional linear Koopman model for the AUV dynamics. Based on the learned linear Koopman model, a tube-based MPC framework consisting of a nominal MPC and an ancillary MPC is designed for AUV trajectory tracking in the presence of disturbances and model uncertainties. Moreover, the stability of the nominal system and the input-to-state stability (ISS) of the actual closed-loop system are rigorously established. Numerical simulation results demonstrate that the proposed method achieves accurate trajectory tracking under disturbances and uncertainties, while significantly reducing the online computational burden compared with nonlinear model predictive control (NMPC).