Weighted Online Koopman Learning for Model Predictive Control of Thrust-Vectored Underwater Vehicles

Underwater vehicles face control challenges including hydrodynamic parameter uncertainties and environmental disturbances. While Koopman-based model predictive control (Koopman-MPC) offers computational efficiency through linear lifted representations, existing methods rely on offline-collected datasets and thus struggle to adapt to the aforementioned challenges. This letter proposes a weighted online Koopman-MPC framework that achieves trajectory tracking through online learning. First, we construct physical information basis functions, explicitly embedding the Coriolis, damping, and restoring force terms into the Koopman lifted space. Second, a weighted incremental Extended Dynamic Mode Decomposition (EDMD) scheme fuses offline data with real-time measurements via a tunable parameter. Finally, an incremental MPC scheme is designed to optimize the control increments to satisfy the actuator rate constraints. Experimental validation on a thrust-vectored underwater vehicle demonstrates that the proposed framework effectively adapts to changing dynamics during operation, improving trajectory tracking accuracy over both the offline model and uniform online updates.