A Tutorial on Gaussian Process Learning-based Model Predictive Control

This tutorial provides a systematic introduction to Gaussian process learning-based model predictive control (GP-MPC), an advanced approach integrating Gaussian process (GP) with model predictive control (MPC) for enhanced control in complex systems. It begins with GP regression fundamentals, illustrating how it enriches MPC with enhanced predictive accuracy and robust handling of uncertainties. A central contribution of this tutorial is the first detailed, systematic mathematical formulation of GP-MPC in literature, focusing on deriving the approximation of means and variances propagation for GP multi-step predictions. Practical applications in robotics control, such as path-following for mobile robots in challenging terrains and mixed-vehicle platooning, are discussed to demonstrate the real-world effectiveness and adaptability of GP-MPC. This tutorial aims to make GP-MPC accessible to researchers and practitioners, enriching the learning-based control field with in-depth theoretical and practical insights and fostering further innovations in complex system control.