Bringing a multilink pendulum to the equilibrium position using a single control torque

The problem of controlling the multilink pendulum in the neighborhood of a given equilibrium position is considered. A feedback control bringing the pendulum to the equilibrium position in a finite time using a bounded torque applied to the first link is constructed. The proposed approach is based on stability theory of motion and uses the concept of the Lyapunov function that is common for two different stable systems of differential equations. The efficiency of the control is demonstrated by a computer simulation of the three-link pendulum dynamics.