Variable structure disturbance rejection control for nonlinear uncertain systems with state and control delays via optimal sliding mode surface approach
type: Item
instance of: scholarly article
title: Variable structure disturbance rejection control for nonlinear uncertain systems with state and control delays via optimal sliding mode surface approach
zbMATH Open document ID: 1295.93021
DOI: 10.1155/2013/141058
author: Jing Lei
author: Xin Wang
author: Yu-Mei She
author: Tian-Jun Zhang
published in: Abstract and Applied Analysis
publication date: 2014-06-20T00:00:00Z
review text: Summary: The paper considers the problem of variable structure control for nonlinear systems with uncertainty and time delays under persistent disturbance by using the optimal sliding mode surface approach. Through functional transformation, the original time-delay system is transformed into a delay-free one. The approximating sequence method is applied to solve the nonlinear optimal sliding mode surface problem which is reduced to a linear two-point boundary value problem of approximating sequences. The optimal sliding mode surface is obtained from the convergent solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. Then, the variable structure disturbance rejection control is presented by adopting an exponential trending law, where the state and control memory terms are designed to compensate the state and control delays, a feedforward control term is designed to reject the disturbance, and an adjoint compensator is designed to compensate the effects generated by the nonlinearity and the uncertainty. Furthermore, an observer is constructed to make the feedforward term physically realizable, and thus the dynamical observer-based dynamical variable structure disturbance rejection control law is produced. Finally, simulations are demonstrated to verify the effectiveness of the presented controller and the simplicity of the proposed approach.
Mathematics Subject Classification ID: 93B12
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C41
zbMATH DE Number: 6306058
zbMATH Keywords: variable structure control
zbMATH Keywords: nonlinear systems with uncertainty and time delays
zbMATH Keywords: persistent disturbance
zbMATH Keywords: optimal sliding mode surface approach
zbMATH Keywords: Riccati equation
zbMATH Keywords: Sylvester equation
zbMATH Keywords: state and adjoint vector differential equation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/141058
OpenAlex ID: W2106646964
Wikidata QID: Q58915351
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description: scientific article; zbMATH DE number 6306058