Design of global smooth implicit control Lyapunov function for multiple-integrator system with input constraint
type: Item
instance of: scholarly article
title: Design of global smooth implicit control Lyapunov function for multiple-integrator system with input constraint
zbMATH Open document ID: 1461.93450
author: Yuh Yamashita
author: Naoto Adachi
author: Ryo Nonaka
author: Koichi Kobayashi
published in: Systems \& Control Letters
publication date: 2021-01-06T00:00:00Z
review text: In order to deal with multiple-integrator systems with input constraints and with a variety of restrictions on the virtual input for the backstepping method, the authors modify the approach of [\textit{A. Polyakov} et al., Automatica 51, 332--340 (2015; Zbl 1309.93135)] to obtain a smooth Lyapunov functional and a smooth controller, in exchange for homogeneity and finite-time stability requirements being dropped. The newly introduced controller is almost linear with respect to the state near the origin, while approximating the homogeneous controller obtained via the implicit Lyapunov function method of [loc. cit.] far from the origin. A bounded virtual control law is then obtained using a transformation on the restricted virtual input, no boundedness condition on the actual input being needed. It is also observed that the proposed method can be combined with bounded-input backstepping methods to obtain a bounded feedback law provided that certain additional assumptions are satisfied. The proposed implicit control Lyapunov function is then applied to the stabilizing control of a magnetic levitation system, the advantages of the approach being highlighted.
reviewed by: Paul Georgescu
Mathematics Subject Classification ID: 93D30
Mathematics Subject Classification ID: 93C95
zbMATH DE Number: 7290544
zbMATH Keywords: input constraints
zbMATH Keywords: control Lyapunov function
zbMATH Keywords: implicit Lyapunov function
zbMATH Keywords: backstepping method
MaRDI profile type: Publication
full work available at URL: j.sysconle.2020.104776
OpenAlex ID: W3084451159
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DOI: 10.1016/J.SYSCONLE.2020.104776
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description: scientific article; zbMATH DE number 7290544