Stabilization Of Cart Pole System

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An inverted pendulum is a simple pendulum held at upright position. A simple pendulum has two equilibrium points: when centre of gravity (CG) of pendulum is right below the pivot point (stable equilibrium) and when CG of pendulum is right above the pivot point (unstable equilibrium). Balancing a simple pendulum at unstable equilibrium point describes the inverted pendulum stabilization problem. Expected complexities while solving this problem include different variations, like commanding the motion of the cart while keeping the pendulum erected (stable). Among the major practical implementation of inverted pendulum is rocket or missile guidance, which is based on thrust actuation at the bottom of the vehicle.