Interesting Topic Ideas for Non-Linear Programming

Question

I am looking for interesting topics to follow with the following 4 topics

1. Dynamic programming,
2. Policy iteration algorithm,
3. Pontryagin maximum principle,
4. Hamilton-Jacobi-Bellman equation.

For example, with the Dynamic Programming one, I could do a Car Racing. As seen in this photo DP for Car Racing. Obviously very simplified but what topics do you think would best demo each of the problems