Multivariable Super-Twisting Algorithm for Systems with Uncertain Input Matrix and Perturbations

Jaime A. Moreno; Hector Rios; Luis Ovalle; Leonid Fridman

doi:10.1109/TAC.2021.3130880

Multivariable Super-Twisting Algorithm for Systems with Uncertain Input Matrix and Perturbations

Jaime A. Moreno, Hector Rios, Luis Ovalle, Leonid Fridman

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

Abstract

This paper proposes a Lyapunov approach to the design of a multivariable generalized Super-Twisting algorithm (MGSTA), which is able to control a system with perturbations and uncertain control matrix, both depending on time and the system states. The presented procedure shows that, under reasonable assumptions for the uncertainties, it is always possible to find a set of constant gains for the MGSTA in order to ensure global and robust finite-time stability of the system's outputs. Simulation results on an omnidirectional mobile robot illustrate the performance of the MGSTA.

Original language	English
Journal	IEEE Transactions on Automatic Control
DOIs	https://doi.org/10.1109/TAC.2021.3130880
State	Accepted/In press - 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
IEEE

Keywords

Convergence
Jacobian matrices
Mobile robots
Perturbation methods
Robust control
Sliding-mode control
Super-Twisting algorithm
Symmetric matrices
Transmission line matrix methods
Uncertain systems
Wheels

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10.1109/TAC.2021.3130880

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title = "Multivariable Super-Twisting Algorithm for Systems with Uncertain Input Matrix and Perturbations",

abstract = "This paper proposes a Lyapunov approach to the design of a multivariable generalized Super-Twisting algorithm (MGSTA), which is able to control a system with perturbations and uncertain control matrix, both depending on time and the system states. The presented procedure shows that, under reasonable assumptions for the uncertainties, it is always possible to find a set of constant gains for the MGSTA in order to ensure global and robust finite-time stability of the system's outputs. Simulation results on an omnidirectional mobile robot illustrate the performance of the MGSTA.",

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author = "Moreno, {Jaime A.} and Hector Rios and Luis Ovalle and Leonid Fridman",

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year = "2021",

doi = "10.1109/TAC.2021.3130880",

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journal = "IRE Transactions on Automatic Control",

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T1 - Multivariable Super-Twisting Algorithm for Systems with Uncertain Input Matrix and Perturbations

AU - Moreno, Jaime A.

AU - Rios, Hector

AU - Ovalle, Luis

AU - Fridman, Leonid

N1 - Publisher Copyright: IEEE

PY - 2021

Y1 - 2021

N2 - This paper proposes a Lyapunov approach to the design of a multivariable generalized Super-Twisting algorithm (MGSTA), which is able to control a system with perturbations and uncertain control matrix, both depending on time and the system states. The presented procedure shows that, under reasonable assumptions for the uncertainties, it is always possible to find a set of constant gains for the MGSTA in order to ensure global and robust finite-time stability of the system's outputs. Simulation results on an omnidirectional mobile robot illustrate the performance of the MGSTA.

AB - This paper proposes a Lyapunov approach to the design of a multivariable generalized Super-Twisting algorithm (MGSTA), which is able to control a system with perturbations and uncertain control matrix, both depending on time and the system states. The presented procedure shows that, under reasonable assumptions for the uncertainties, it is always possible to find a set of constant gains for the MGSTA in order to ensure global and robust finite-time stability of the system's outputs. Simulation results on an omnidirectional mobile robot illustrate the performance of the MGSTA.

KW - Convergence

KW - Jacobian matrices

KW - Mobile robots

KW - Perturbation methods

KW - Robust control

KW - Sliding-mode control

KW - Super-Twisting algorithm

KW - Symmetric matrices

KW - Transmission line matrix methods

KW - Uncertain systems

KW - Wheels

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U2 - 10.1109/TAC.2021.3130880

DO - 10.1109/TAC.2021.3130880

M3 - Artículo

AN - SCOPUS:85120544282

JO - IRE Transactions on Automatic Control

JF - IRE Transactions on Automatic Control

SN - 0018-9286

ER -

Multivariable Super-Twisting Algorithm for Systems with Uncertain Input Matrix and Perturbations

Abstract

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Keywords

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