Dynamics and stability state-space of a controlled inverted pendulum (Q2564419)

We study the dynamics of an inverted pendulum under the regulation of a linear-feedback control system. Analysis of the dynamic equations indicates the presence of stable regions in the four-dimensional state space of the system, which is confirmed through simulations. System trajectories are examined in this state space, and complex, apparently chaotic behaviour is observed outside the stable regions. An algorithm is developed to map the boundary of the stable state-space hyper-volume. This boundary exhibits a jagged, possibly fractal, morphology.