Forced oscillations and control of an inverted pendulum

In the talk, we will discuss some general properties of the vector field of an inverted pendulum with a horizontally moving pivot point and will show how these properties can be used to prove the existence of a forced oscillation in the system and to explain the impossibility of global stabilization of the pendulum in the vertical upward position. We will also spend some time discussing further generalizations of the considered methods and ideas. For instance, similarly to the case of one inverted pendulum, it can be shown that there exists a forced oscillation in the system of a chain of strongly coupled pendulums with non-local interaction in a periodic field.