A formula for iterated derivatives along trajectories of nonlinear systems
type: Item
instance of: scholarly article
title: A formula for iterated derivatives along trajectories of nonlinear systems
zbMATH Open document ID: 0647.93034
DOI: 10.1016/0167-6911(88)90104-1
published in: Systems \& Control Letters
publication date: 1988-01-01T00:00:00Z
review text: A study is made of the iterated time derivative of the output y(t) of a nonlinear control system of the form \(\dot x=f(x)+g(x)u\), \(y=h(x)\) is given. The expression of the k-th order time derivative of y(t) as a function of the time derivatives of u(t) involves calculations in noncommuting variables. This approach is very much in line with the so called Fliess-expansion for y(t) as a sum of noncommuting iterated integrals of u; see \textit{M. Fliess}, Bull. Soc. Math. Fr. 109, 3-40 (1981; Zbl 0476.93021).
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 16Y99
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 28A15
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 4057390
zbMATH Keywords: iterated time derivative
zbMATH Keywords: nonlinear control system
zbMATH Keywords: noncommuting variables
author: Françoise Lamnabhi-Lagarrigue
author: Peter E. Crouch
reviewed by: H. Nijmeijer
MaRDI profile type: Publication
full work available at URL: 0167-6911(88)90104-1
OpenAlex ID: W1984429754
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description: scientific article; zbMATH DE number 4057390