Global-stabilization of the inverted-pendulum; an early solution and hardware implementation

The problem of globally stabilizing an inverted-pendulum with arbitrary initial conditions and with the pivot mounted on a movable platform constrained to move in horizontal motion and controlled by a servomotor is considered. A novel solution involving a dual-mode optimal control-law consisting of a bang-bang, time-optimal mode and a smooth linear mode is developed. The results are verified in a full, non-linear simulation as well as implemented in an actual hardware model. These results appear in a Master's Thesis written in 1971 and apparently predate similar results reported in the literature.