These are notes for the tutorials of the subject "Optimal and Predictive Control System" taught at the Faculty of Mechanical Engineering at the Czech Technical University in Prague.
The materials are loosely divided into three blocks. The first focuses on the classical approaches in optimal control, namely the four basic variants of the linear quadratic regulator (LQR) which are derived from the Bellman principle. The second goes over the basics of numerical optimization building up-to the third and final block focusing on model predictive control (MPC).
DISCLAIMER: These notes have not gone through a peer review process and are likely to contain (hopefully only minor) mistakes.