  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.
