Video Library
Most viewed videos

New in collection

You may need the following programs to see the files

Scientific session of the Steklov Mathematical Institute of RAS dedicated to the results of 2018
November 21, 2018 11:00–11:15, Moscow, Steklov Mathematical Institute of RAS, Conference Hall (8 Gubkina)

On topological obstructions to global stabilization of an inverted pendulum

I. Yu. Polekhin
Video records:
MP4 408.3 Mb
MP4 185.5 Mb

Number of views:
This page:99
Video files:29

I. Yu. Polekhin
Photo Gallery

Видео не загружается в Ваш браузер:
  1. Установите Adobe Flash Player    

  2. Проверьте с Вашим администратором, что из Вашей сети разрешены исходящие соединения на порт 8080
  3. Сообщите администратору портала о данной ошибке

Abstract: If the configuration space of a controlled system is closed, the feedback control is autonomous and solutions exist, unique, and continuously depend on the initial data, then the system cannot have a globally asymptotically stable equilibrium. It follows from the fact that a closed manifold cannot be contractible. Let us consider a classical controlled system, an inverted pendulum controlled by means of a horizontal motion of its pivot point. We consider the pendulum only in the positions where its mass point is above the pivot point (for instance, we can consider any mechanical model of the rod-plane impact). Although the configuration space in this case is contractible, we prove that, for any mechanical model of the impact, it is impossible to globally stabilize the rod in a given position (we also assume some natural properties of the equilibrium). To be more precise, we prove that there always exists a family of solutions separated from the vertical position and along which the pendulum never becomes horizontal. Similar results can be easily proved for several analogous systems: a pendulum on a cart, a spherical pendulum, and a pendulum with an additional torque control.

Related articles:

SHARE: FaceBook Twitter Livejournal
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019