A Power Tower Control: A New Sliding Mode Control

TL;DR

This paper introduces a novel sliding mode control based on a power tower function of order 2, enabling guaranteed and finite-time convergence for perturbed double integrator systems without prior knowledge of disturbance bounds.

Contribution

It proposes a new control method combining power tower functions with backstepping, achieving guaranteed and finite-time convergence under different disturbance conditions.

Findings

Control guarantees convergence when disturbance is constant and bounded.

Finite-time convergence is achieved when disturbance is variable with known bounds.

Simulation results validate the effectiveness of the proposed control method.

Abstract

A control based power tower function at order 2 is proposed in this paper. This leads to a new sliding mode control, which allows employing backstepping technique that combines both guaranteed and finite time convergence. The proposed control is applied to a double integrator subject to perturbation $d$. Both guaranteed and finite convergence are ensured by the controller when $d$ is considered constant and bounded, without knowing its upper bound. For the case, when $d$ is variable and bounded with its upper bound known, only a finite time convergence is obtained. Simulation results are given to show the well founded of the proposed novel control.