Gaussian Process Based Learning Model Predictive Control With Application to USV

This article presents a learning model predictive control (LMPC) method for nonlinear systems with additive state-dependent uncertainties. Both the residual part of the system and the observation dynamics are modeled as Gaussian process regression (GPR), respectively. First, the predicting residual part is used to complement the nominal model. Second, the Gaussian process-based extended Kalman filter (GP-EKF) is formulated by integrating the augmented system dynamics and the differentiable GPR-type observation dynamics to refine the observed states. To alleviate the computational load, the event-triggered criteria are designed to select the training data, and a hybrid warm start scheme is developed to initialize the optimization problem. Furthermore, the closed-loop stability is theoretically analyzed. Finally, the effectiveness of the designed LMPC algorithm with GP-EKF is verified by trajectory tracking of unmanned surface vehicle via simulation and hardware experiments.