Not sure if I am posting this question in the correct community, as it relates primarily to reinforcement learning. Apologies early on if this is not so.
In reinforcement learning many algorithms exist for 'solving' the cart-pole problem; that of balancing a mass on the edge of a stick, connected to a cart on a hinge, which has 1 DoF. There is TD learning, Q-learning and many other on and off-policy methods. There is also the more recent, model-based policy search method PILCO.
What I am really wondering, I suppose, is more of a physics question: is there a need for active control? Why is it not possible to find the one point for the cart, which prevents the mass to move, even incrementally, left or right as it sits atop the pole? Why does it always 'fall'?