I wrote short notes on the 1D LQR which hopefully will help you understand better the material introduced in tutorial 2 of W2D4. Check it out if you were wondering about any of these:
(1) How to derive the optimal control gain?
(2) What is the relation to the linear systems studied during W2D2?
(3) Can reinforcement learning (W2D5) be applied to the LQR problem?
Let me know if you have any questions or if you find any mistakes!