Tutorial on Predictive Control for Systems With Model Uncertainty Using Gaussian Process Regression

This study presents a method to improve control performance in complex dynamic systems by integrating Gaussian processes (GP) and model predictive control (MPC). GP enables learning from nonlinear systems without explicit models, while MPC can integrate the learned models to generate optimal control policies. Approximation techniques such as sparse GP, which focus on computational efficiency, are introduced to address the high computational load of GP. Furthermore, experimental and comparative analyses consistently show that GP-based MPC surpasses traditional nominal model-based methods in controlling nonlinear systems, especially in terms of tracking accuracy, robustness to uncertainties, and effective handling of unmodeled dynamics. This article highlights the theoretical background, computational considerations, and practical applications of GP–MPC, providing a foundation for exploration of learning-based control systems.