Optimal Lyapunov-Based Reaching Time Bounds for the Super-Twisting Algorithm

Richard Seeber; Martin Horn

doi:10.1109/LCSYS.2019.2920163

Optimal Lyapunov-Based Reaching Time Bounds for the Super-Twisting Algorithm

Richard Seeber, Martin Horn

Institute of Automation and Control (4430)

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

Abstract

The super-twisting algorithm is a second order sliding mode control law commonly used for robust control and observation. One of its key properties is the finite time it takes to reach the sliding surface. Using Lyapunov theory, upper bounds for this reaching time may be found. This contribution considers the problem of finding the best bound that may be obtained using a family of quadratic Lyapunov functions. An optimization problem for finding this bound is derived, whose solution may be obtained using semidefinite programming. It is shown that the restrictions imposed on the perturbations and the conservativeness of the obtained bound are significantly reduced compared to existing results from literature.

Original language	English
Pages (from-to)	924-929
Journal	IEEE Control Systems Letters
Volume	3
Issue number	4
DOIs	https://doi.org/10.1109/LCSYS.2019.2920163
Publication status	Published - 2019
Event	58th Conference on Decision and Control - Nice, France Duration: 11 Dec 2019 → 13 Dec 2019

Keywords

Sliding mode control
Convergence time
Lyapunov functions
Optimisation
Linear matrix inequalities
optimization
convergence time
LMIs
Variable-structure/sliding-mode control

ASJC Scopus subject areas

Control and Optimization
Control and Systems Engineering

Access to Document

10.1109/LCSYS.2019.2920163

accepted_articleAccepted author manuscript, 423 KBLicence: CC BY-NC-ND 4.0

Cite this

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title = "Optimal Lyapunov-Based Reaching Time Bounds for the Super-Twisting Algorithm",

abstract = "The super-twisting algorithm is a second order sliding mode control law commonly used for robust control and observation. One of its key properties is the finite time it takes to reach the sliding surface. Using Lyapunov theory, upper bounds for this reaching time may be found. This contribution considers the problem of finding the best bound that may be obtained using a family of quadratic Lyapunov functions. An optimization problem for finding this bound is derived, whose solution may be obtained using semidefinite programming. It is shown that the restrictions imposed on the perturbations and the conservativeness of the obtained bound are significantly reduced compared to existing results from literature.",

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language = "English",

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journal = "IEEE Control Systems Letters",

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T1 - Optimal Lyapunov-Based Reaching Time Bounds for the Super-Twisting Algorithm

AU - Seeber, Richard

AU - Horn, Martin

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AB - The super-twisting algorithm is a second order sliding mode control law commonly used for robust control and observation. One of its key properties is the finite time it takes to reach the sliding surface. Using Lyapunov theory, upper bounds for this reaching time may be found. This contribution considers the problem of finding the best bound that may be obtained using a family of quadratic Lyapunov functions. An optimization problem for finding this bound is derived, whose solution may be obtained using semidefinite programming. It is shown that the restrictions imposed on the perturbations and the conservativeness of the obtained bound are significantly reduced compared to existing results from literature.

KW - Sliding mode control

KW - Convergence time

KW - Lyapunov functions

KW - Optimisation

KW - Linear matrix inequalities

KW - optimization

KW - convergence time

KW - LMIs

KW - Variable-structure/sliding-mode control

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DO - 10.1109/LCSYS.2019.2920163

M3 - Article

SN - 2475-1456

VL - 3

SP - 924

EP - 929

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

IS - 4

T2 - 58th Conference on Decision and Control

Y2 - 11 December 2019 through 13 December 2019

ER -

Optimal Lyapunov-Based Reaching Time Bounds for the Super-Twisting Algorithm

Abstract

Keywords

ASJC Scopus subject areas

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