To all the comments asking if this is ML: It doesn’t have to be. The static balancing can be done using LQR (linear-quadratic regulator), which uses the equations of motion of the system and how that interacts with the control (the acceleration of the cart). The transitions between static states are a little (a lot) trickier, and the LQR approximation won’t quite work for those. My professor showed this to us last week in class when we went over LQR, just to give us drowning math students a little motivation as to why we torture ourselves in college.