Add MountainCar-V0 to DynSys

[michael-lauria]

I'm looking into backwards reachability in MountainCar-V0 and was hoping to use this package. Here is my effort so far, but I'm not able to get the reachable set to grow to include the usual starting point at (-0.4, 0). (see video attached)

reach_fail_mountain_car.mp4

If someone has some time to help me out:

1. Is there something obvious that I am doing wrong?
2. Is my choice of optimal control the problem? (assumed it works from https://github.com/openai/gym/wiki/Leaderboard#mountaincar-v0, but could verify somehow?)
3. Any other suggestions at all! Thank you!

EDIT: Here is a video with a denser grid. I am trying to investigate the narrow passage in state space, so this is almost expected, but I'm hoping to see it make it to the other side.

1841_grid.mp4

EDIT 2: I think I managed to fix the optimal control. The latest video is below. I used a grid of 181 x 181 and run for 600 time steps (60 "seconds") . The reachable set still does not approach the initial conditions.

181_grid_new.mp4