Hybrid control for global stabilization of the cart-pendulum system

Abstract

A globally stabilizing controller for the cart-pendulum system is designed in this paper. The design procedure consists of three parts. First, find a neighborhood of the origin in which a locally stabilizing controller can be used. Second, construct a linear controller for the cart subsystem and steer the position and velocity of the cart to the origin. The last part is to design several classes of bang-bang controllers and a switching strategy which guarantee that the trajectory of the system starting from any initial condition enters, in finite times of switching, the neighborhood where the locally stabilizing controller is effective. Show more