Learning a Gaussian Process Approximation of a Model Predictive Controller with Guarantees

Model predictive control effectively handles complex dynamical systems with constraints, but its high computational demand often makes real-time application infeasible. We propose using Gaussian process regression to learn an approximation of the controller offline for online use. Our approach incorporates a robust predictive control scheme and provides bounds on approximation errors to ensure recursive feasibility and input-to-state stability. Exploiting a sampling-based scenario approach, we develop an efficient sampling strategy and guarantee that, with high probability, the approximation error remains within acceptable bounds. Our method demonstrates enhanced efficiency and reduced computational demand in an example application.