GP-based MPC with updating tube for safety control of unknown system

The Gaussian process model inferred from the Bayesian framework is a powerful data modeling method. It pro-vides not only the predictive value but also the uncertainty measure for the predictive result. In this paper, we combine the online-updating GP models with Tube MPC to achieve safety control for the system of unknown dynamics, and especially use its capability of uncertainty quantification to assist in the safety guarantee under certain probability. Tightened constraints for safety used to determine the center of the Tube are computed ac-cording to the designed method based on the mean and variance predictive function of GP models. The constraints are updated at every control period based on the updated GP models. Meanwhile, a specific updating mechanism of the data set is adopted to accomplish effective updating. Finally, an example of a vehicle system model is used to verify the proposed method.