Due Wednesday 3/15 11:59 PM Eastern.

In this homework, we are going to explore LQR, convex trajectory optimization, and convex model predictive control. Here is an overview of the problems:

1. Solve for the finite-horizon LQR controls as a convex optimization problem, then solve for the optimal feedback policy with the Ricatti recursion. Show that these are equivalent.

2. Here we will use TVLQR to track a cartpole swingup, as well as infinite horizon LQR to stabilize the cartpole in the inverted position.

3. In this question we will design controllers using LQR, convex trajectory optimization, and convex MPC for controlling the SpaceX Dragon spacecraft as it rendezvous with the ISS.

Use any method you like to export your jupyter notebook as a PDF (with all the cell outputs shown), and submit on gradescope. Here are some methods for creating this PDF: https://mljar.com/blog/jupyter-notebook-pdf/.