Exact Multiple-Step Predictions in Gaussian Process-based Model Predictive Control: Observations, Possibilities, and Challenges

Employing learned Gaussian process models in nonlinear model predictive control raises the problem of repeatedly propagating a probability distribution through a nonlinear mapping, which is a challenging task. Existing solutions are either computationally expensive or conservative. We propose to use Gaussian process models that directly yield the entire state sequence without repeated evaluations. As therefrom an exact Gaussian distribution is obtained in each step on the prediction horizon, an increased prediction quality is achieved when compared to employing iterated models. The proposed approach is illustrated in a simulation study, where we show the quality gain in the open-loop state predictions, as well as in the closed-loop performance.