Higher order super-twisting algorithm for perturbed chains of integrators of arbitrary order

TL;DR

This paper introduces a generalized higher order super-twisting controller for perturbed integrator chains of any order, extending previous methods with a homogeneous, continuous design based on a Lyapunov function.

Contribution

It develops a new higher order super-twisting algorithm applicable to arbitrary order perturbed integrator chains, with a homogeneous, continuous control law derived from a geometric condition.

Findings

Controller successfully stabilizes perturbed integrator chains of order four.

Simulation results compare two HOST controllers, demonstrating effectiveness.

The approach extends super-twisting methods to higher order systems.

Abstract

In this paper, we present a generalization of the super-twisting algorithm for perturbed chains of integrators of arbitrary order. This Higher Order Super-Twisting (HOST) controller, which extends the approach of Moreno and als., is homegeneous with respect to a family of dilations and can be continuous. Its design is derived from a first result obtained for pure chains of integrators, the latter relying on a geometric condition introduced by the authors. The complete result is established using a homogeneous strict Lyapunov function which is explicitely constructed. The effectiveness of the controller is finally illustrated with simulations for a chain of integrator of order four, first pure then perturbed, where we compare the performances of two HOST controllers.