Explore a comprehensive lecture on learning-based model predictive control and its application in safe learning for control systems. Delve into the intersection of control, learning, and optimization as Melanie Zeilinger from ETH Zurich and University of Freiburg discusses techniques bridging optimization-based control and reinforcement learning. Discover methods for inferring models from data, implementing safety filters, and addressing critical safety constraints in probability. Examine real-world applications in robotics, including examples with race cars, pendulums, and quadrotors. Gain insights into Gaussian processes, Bayesian optimization, and robust model predictive control as tools for achieving high-performance controllers that balance simplicity, efficiency, and safety guarantees.