On modular backstepping design with second order sliding modes
type: Item
instance of: scholarly article
title: On modular backstepping design with second order sliding modes
zbMATH Open document ID: 0964.93017
DOI: 10.1016/S0005-1098(00)00131-X
author: Luisa Giacomini
author: Antonella Ferrara
published in: Automatica
publication date: 2001-06-27T00:00:00Z
review text: The paper deals with systems in the parametric-strict feedback form \[ \begin{aligned} x_i'' &=x_{i+1}+\theta \Phi _i(x_1,\dots ,x_i),\quad i=1,\dots ,n-1, \\ x_n'' &=\Phi _0(x_1,\dots ,x_n)+\theta \Phi _n(x_1,\dots ,x_n)+\beta (x_1,\dots ,x_n)u,\end{aligned} \] where \(\theta \) is a vector of constant unknown parameters, \(\Phi _i\) and \( \beta \) are known smooth nonlinear functions. The control objective is to make \(\gamma =x_1(t)\) track a smooth reference trajectory \(\gamma _r(t).\) A modular procedure to design estimation-based second order sliding mode controllers for uncertain nonlinear systems expressible in parametric-strict feedback form is presented. It consists of \(n-2\) steps of modular backstepping to compute all the quantities needed to build a second order auxiliary system. In particular, the authors propose a desired algorithm which is a modification of the Bartolini algorithm [\textit{G. Bartolini, A. Ferrara} and \textit{E. Usai}, Int. J. Robust Nonlinear Control 7, 299-319 (1997)]. Convergence of the desired algorithm is proved. A numerical example is considered.
Mathematics Subject Classification ID: 93B12
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93B51
zbMATH DE Number: 1553209
zbMATH Keywords: adaptive controller
zbMATH Keywords: robust control
zbMATH Keywords: algorithm
zbMATH Keywords: discretization
zbMATH Keywords: Lyapunov function
zbMATH Keywords: tracking
zbMATH Keywords: parametric-strict feedback form
zbMATH Keywords: second order sliding mode
zbMATH Keywords: backstepping
Wikidata QID: Q59909102
MaRDI profile type: Publication
cites work: APPLICATIONS OF A SUB-OPTIMAL DISCONTINUOUS CONTROL ALGORITHM FOR UNCERTAIN SECOND ORDER SYSTEMS
cites work: Output tracking control of uncertain nonlinear second-order systems
cites work: Q4398294
cites work: Adaptive sliding mode control in discrete-time systems
cites work: Design of `softer' robust nonlinear control laws
cites work: Adaptive nonlinear control without overparametrization
cites work: Adaptive nonlinear design with controller-identifier separation and swapping
cites work: Global stability of parameter-adaptive control systems
cites work: Smooth stabilization implies coprime factorization
cites work: A canonical expansion for nonlinear systems
cites work: Sliding modes in control and optimization. Transl. from the Russian
cites work: Multiple-surface sliding control of a class of uncertain nonlinear systemsm
full work available at URL: s0005-1098(00)00131-x
OpenAlex ID: W2000308029
DBLP publication ID: journals/automatica/FerraraG01
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description: scientific article; zbMATH DE number 1553209