Discontinuous integral control for mechanical systems

TL;DR

This paper introduces a discontinuous integral control scheme for mechanical systems that achieves finite-time tracking of unknown signals, is robust against bounded derivative perturbations, and ensures global stability with a smooth Lyapunov function.

Contribution

It presents a novel discontinuous integral controller combined with a velocity observer for finite-time, robust output tracking in mechanical systems.

Findings

Controller achieves finite-time convergence.

System is robust to bounded derivative perturbations.

Global stability is proven using a new Lyapunov function.

Abstract

For mechanical systems we present a controller able to track an unknown smooth signal, converging in finite time and by means of a continuous control signal. The control scheme is insensitive against unknown perturbations with bounded derivative. The controller consists of a non locally Lipschitz state feedback control law, and a discontinuous integral controller, that is able to estimate the unknown perturbation and to compensate for it. To complete an output feedback control a continuous observer for the velocity is added. It is shown that the closed loop consisting of state feedback, state observer and discontinuous integral controller has an equilibrium point that is globally, finite time stable, despite of perturbations with bounded derivative. The proof is based on a new smooth Lyapunov function.