A Topological View on Forced Oscillations and Control of an Inverted Pendulum

  • Ivan Polekhin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10589)


We consider a system of a planar inverted pendulum in a gravitational field. First, we assume that the pivot point of the pendulum is moving along a horizontal line with a given law of motion. We prove that, if the law of motion is periodic, then there always exists a periodic solution along which the pendulum never becomes horizontal (never falls). We also consider the case when the pendulum with a moving pivot point is a control system, in which the mass point is constrained to be strictly above the pivot point (the rod cannot fall ‘below the horizon’). We show that global stabilization of the vertical upward position of the pendulum cannot be obtained for any smooth control law, provided some natural assumptions.


Inverted pendulum Forced oscillations Global stabilization Control design 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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