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.
@article{arxiv.2405.14461,
title = {A Power Tower Control: A New Sliding Mode Control},
author = {Malek Ghanes and Jean-Pierre Barbot},
journal= {arXiv preprint arXiv:2405.14461},
year = {2024}
}