Barrier Function-Based Adaptive Continuous Higher-Order Sliding Mode Controllers with Unbounded Perturbations

TL;DR

This paper introduces two types of continuous higher-order adaptive sliding mode controllers using barrier functions for systems with unbounded perturbations, ensuring finite-time convergence with either unbounded or bounded control gains.

Contribution

The paper develops novel barrier function-based adaptive controllers for perturbed systems, including a new adaptive higher order Super-Twisting algorithm with bounded gains under Lipschitz conditions.

Findings

Finite-time convergence of system states achieved

Unbounded control gains possible without perturbation assumptions

Bounded control gains ensured for Lipschitz perturbations

Abstract

In this paper, two classes of continuous higher order adaptive sliding mode controllers based on barrier functions are developed for a perturbed chain of integrators with unbounded perturbations. Both classes provide finite-time convergence of system states to a predefined domain using a continuous control signal. The first class of adaptive controllers does not require any assumptions about the perturbation; however, it can provide unbounded control gains. To ensure bounded control gains, and in the case of a Lipschitz perturbation, a second class of adaptive controllers, called the adaptive higher order Super-Twisting (HOST) algorithm, is developed.