Implicit Discrete-Time Adaptive First-Order Sliding Mode Control with Predefined Convergence Time

Xiaogang Xiong; Hua Chen; Yunjiang Lou; Zhichao Liu; Shyam Kamal; Motoji Yamamoto

doi:10.1109/TCSII.2021.3070435

Implicit Discrete-Time Adaptive First-Order Sliding Mode Control with Predefined Convergence Time

Xiaogang Xiong
, Hua Chen
, Yunjiang Lou^*
, Zhichao Liu
, Shyam Kamal
, Motoji Yamamoto

^*Corresponding author for this work

Harbin Institute of Technology Shenzhen
Kyushu University
Ubtech Company
Indian Institute of Technology Banaras Hindu University

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

12 Scopus citations

Abstract

This brief proposes an adaptive first-order sliding mode control (SMC) with a predefined convergence time in a digital framework. It is based on an implicit Euler discretization of the set-valued signum function in SMC and a time-dependent adaptive gain scheme. Two typical cases are discussed and their stability analysis is provided, simple affine systems with first-order SMC and LTI systems with equivalent control-based sliding mode control (ECB-SMC), both in the presence of unknown perturbations. Numerical simulations show that, compared with the conventional SMC, the proposed implicit discrete-time SMC guarantees the convergence of the states within any predefined arbitrary time.

Original language	English
Pages (from-to)	3562-3566
Number of pages	5
Journal	IEEE Transactions on Circuits and Systems II: Express Briefs
Volume	68
Issue number	12
DOIs	https://doi.org/10.1109/TCSII.2021.3070435
State	Published - 1 Dec 2021
Externally published	Yes

Keywords

Super-twisting observer
arbitrary convergence time
chattering
implicit Euler

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10.1109/TCSII.2021.3070435

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title = "Implicit Discrete-Time Adaptive First-Order Sliding Mode Control with Predefined Convergence Time",

abstract = "This brief proposes an adaptive first-order sliding mode control (SMC) with a predefined convergence time in a digital framework. It is based on an implicit Euler discretization of the set-valued signum function in SMC and a time-dependent adaptive gain scheme. Two typical cases are discussed and their stability analysis is provided, simple affine systems with first-order SMC and LTI systems with equivalent control-based sliding mode control (ECB-SMC), both in the presence of unknown perturbations. Numerical simulations show that, compared with the conventional SMC, the proposed implicit discrete-time SMC guarantees the convergence of the states within any predefined arbitrary time.",

keywords = "Super-twisting observer, arbitrary convergence time, chattering, implicit Euler",

author = "Xiaogang Xiong and Hua Chen and Yunjiang Lou and Zhichao Liu and Shyam Kamal and Motoji Yamamoto",

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AU - Xiong, Xiaogang

AU - Chen, Hua

AU - Lou, Yunjiang

AU - Liu, Zhichao

AU - Kamal, Shyam

AU - Yamamoto, Motoji

PY - 2021/12/1

Y1 - 2021/12/1

N2 - This brief proposes an adaptive first-order sliding mode control (SMC) with a predefined convergence time in a digital framework. It is based on an implicit Euler discretization of the set-valued signum function in SMC and a time-dependent adaptive gain scheme. Two typical cases are discussed and their stability analysis is provided, simple affine systems with first-order SMC and LTI systems with equivalent control-based sliding mode control (ECB-SMC), both in the presence of unknown perturbations. Numerical simulations show that, compared with the conventional SMC, the proposed implicit discrete-time SMC guarantees the convergence of the states within any predefined arbitrary time.

AB - This brief proposes an adaptive first-order sliding mode control (SMC) with a predefined convergence time in a digital framework. It is based on an implicit Euler discretization of the set-valued signum function in SMC and a time-dependent adaptive gain scheme. Two typical cases are discussed and their stability analysis is provided, simple affine systems with first-order SMC and LTI systems with equivalent control-based sliding mode control (ECB-SMC), both in the presence of unknown perturbations. Numerical simulations show that, compared with the conventional SMC, the proposed implicit discrete-time SMC guarantees the convergence of the states within any predefined arbitrary time.

KW - Super-twisting observer

KW - arbitrary convergence time

KW - chattering

KW - implicit Euler

UR - https://www.scopus.com/pages/publications/85103772466

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JO - IEEE Transactions on Circuits and Systems II: Express Briefs

JF - IEEE Transactions on Circuits and Systems II: Express Briefs

IS - 12

ER -

Implicit Discrete-Time Adaptive First-Order Sliding Mode Control with Predefined Convergence Time

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Keywords

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