A Novel Method to Estimate the Reaching Time of the Super-Twisting Algorithm

Richard Seeber, Martin Horn, Leonid Fridman

Research output: Contribution to journal › Article › Research › peer-review

Abstract

The super-twisting algorithm is a well-known technique in the field of sliding mode control or observation. In this contribution, an exact analytic expression for this algorithm's finite reaching time in the unperturbed case is derived. Based on this derivation, a novel estimation for the upper bound of the algorithm's reaching time the presence of perturbations is presented. The considered perturbations may be composed of additive components that are either Lipschitz continuous in time or Hölder continuous in the sliding variable. Both analytically and in the course of numerical examples the new strategy is shown to yield significant improvements compared to existing reaching time estimates.
Original languageEnglish
Pages (from-to)4301-4308
JournalIEEE Transactions on Automatic Control
Volume63
Issue number12
DOIs
Publication statusPublished - 2018

Fingerprint

Sliding mode control

Keywords

  • Lyapunov function
  • Reaching time
  • Sliding mode control

Fields of Expertise

  • Information, Communication & Computing

Cite this

A Novel Method to Estimate the Reaching Time of the Super-Twisting Algorithm. / Seeber, Richard; Horn, Martin; Fridman, Leonid.

In: IEEE Transactions on Automatic Control, Vol. 63, No. 12, 2018, p. 4301-4308.

Research output: Contribution to journal › Article › Research › peer-review

Seeber, R, Horn, M & Fridman, L 2018, 'A Novel Method to Estimate the Reaching Time of the Super-Twisting Algorithm' IEEE Transactions on Automatic Control, vol. 63, no. 12, pp. 4301-4308. https://doi.org/10.1109/TAC.2018.2812789
Seeber R, Horn M, Fridman L. A Novel Method to Estimate the Reaching Time of the Super-Twisting Algorithm. IEEE Transactions on Automatic Control. 2018;63(12):4301-4308. https://doi.org/10.1109/TAC.2018.2812789
Seeber, Richard ; Horn, Martin ; Fridman, Leonid. / A Novel Method to Estimate the Reaching Time of the Super-Twisting Algorithm. In: IEEE Transactions on Automatic Control. 2018 ; Vol. 63, No. 12. pp. 4301-4308.
@article{7bada129cbab4c73b6421825cac727e9,
title = "A Novel Method to Estimate the Reaching Time of the Super-Twisting Algorithm",
abstract = "The super-twisting algorithm is a well-known technique in the field of sliding mode control or observation. In this contribution, an exact analytic expression for this algorithm's finite reaching time in the unperturbed case is derived. Based on this derivation, a novel estimation for the upper bound of the algorithm's reaching time the presence of perturbations is presented. The considered perturbations may be composed of additive components that are either Lipschitz continuous in time or H{\"o}lder continuous in the sliding variable. Both analytically and in the course of numerical examples the new strategy is shown to yield significant improvements compared to existing reaching time estimates.",
keywords = "Lyapunov function, Reaching time, Sliding mode control",
author = "Richard Seeber and Martin Horn and Leonid Fridman",
year = "2018",
doi = "10.1109/TAC.2018.2812789",
language = "English",
volume = "63",
pages = "4301--4308",
journal = "IEEE Transactions on Automatic Control",
issn = "0018-9286",
publisher = "IEEE Control Systems Society",
number = "12",

}

TY - JOUR

T1 - A Novel Method to Estimate the Reaching Time of the Super-Twisting Algorithm

AU - Seeber, Richard

AU - Horn, Martin

AU - Fridman, Leonid

PY - 2018

Y1 - 2018

N2 - The super-twisting algorithm is a well-known technique in the field of sliding mode control or observation. In this contribution, an exact analytic expression for this algorithm's finite reaching time in the unperturbed case is derived. Based on this derivation, a novel estimation for the upper bound of the algorithm's reaching time the presence of perturbations is presented. The considered perturbations may be composed of additive components that are either Lipschitz continuous in time or Hölder continuous in the sliding variable. Both analytically and in the course of numerical examples the new strategy is shown to yield significant improvements compared to existing reaching time estimates.

AB - The super-twisting algorithm is a well-known technique in the field of sliding mode control or observation. In this contribution, an exact analytic expression for this algorithm's finite reaching time in the unperturbed case is derived. Based on this derivation, a novel estimation for the upper bound of the algorithm's reaching time the presence of perturbations is presented. The considered perturbations may be composed of additive components that are either Lipschitz continuous in time or Hölder continuous in the sliding variable. Both analytically and in the course of numerical examples the new strategy is shown to yield significant improvements compared to existing reaching time estimates.

KW - Lyapunov function

KW - Reaching time

KW - Sliding mode control

U2 - 10.1109/TAC.2018.2812789

DO - 10.1109/TAC.2018.2812789

M3 - Article

VL - 63

SP - 4301

EP - 4308

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 12

ER -

Access to Document