Backstepping for nonsmooth systems
type: Item
instance of: scholarly article
title: Backstepping for nonsmooth systems
zbMATH Open document ID: 1029.93053
DOI: 10.1016/S0005-1098(03)00081-5
author: Herbert G. Tanner
author: Kostas J. Kyriakopoulos
published in: Automatica
publication date: 2003-07-29T00:00:00Z
review text: The paper presents a smooth version of the backstepping stabilization method. More precisely, the authors consider the system \[ \begin{cases} \dot\eta= f(\eta)+ g(\eta)\xi\\\;\xi=u \end{cases} \] under the assumption that the first subsystem is stabilized by a possibly discontinuous feedback \(\xi=\varphi (\eta)\) (the solutions of the closed-loop system are intended in Filippov's sense). Making use of the Clarke generalized directional derivative, they provide an explicit expression for a stabilizer \(u=\psi (\eta,\xi)\) of the overall system. As illustrative examples, they discuss the case of a mobile robot and the case of the electronic throttle control.
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 34A36
zbMATH DE Number: 1956150
zbMATH Keywords: Filippov solution
zbMATH Keywords: backstepping
zbMATH Keywords: nonholonomic systems
zbMATH Keywords: nonsmooth differential equations
zbMATH Keywords: discontinuous control
zbMATH Keywords: Clarke generalized directional derivative
zbMATH Keywords: mobile robot
zbMATH Keywords: electronic throttle control
reviewed by: Andrea Bacciotti
MaRDI profile type: Publication
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full work available at URL: s0005-1098(03)00081-5
OpenAlex ID: W2035860158
description: scientific article; zbMATH DE number 1956150