High order approximation of implicitly defined maps

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Approximations for the function φ{symbol} implicitly defined by φ{symbol}(u)=Φ(u, φ{symbol}(u)) are obtained via the iterative scheme φ{symbol}n(u)=Φ(u, φ{symbol}n-1(u)). In this paper the uniform convergence of high order derivatives of φ{symbol}n to the corresponding derivatives of φ{symbol} is proved. This result yields a high order approximation theorem for the input-output map generated by a nonlinear control system, using linear combinations of iterated integrals of the control.

Original languageEnglish (US)
Pages (from-to)163-173
Number of pages11
JournalAnnali di Matematica Pura ed Applicata
Volume137
Issue number1
DOIs
StatePublished - Dec 1 1984

Fingerprint

Higher Order Approximation
Derivatives
Nonlinear control systems
Iterated integral
Nonlinear Control Systems
Higher order derivative
Approximation Theorem
Uniform convergence
Iterative Scheme
Linear Combination
Derivative
Output
Approximation

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

@article{13a28573522b4bb297ef0d8ec4ec1c1d,
title = "High order approximation of implicitly defined maps",
abstract = "Approximations for the function φ{symbol} implicitly defined by φ{symbol}(u)=Φ(u, φ{symbol}(u)) are obtained via the iterative scheme φ{symbol}n(u)=Φ(u, φ{symbol}n-1(u)). In this paper the uniform convergence of high order derivatives of φ{symbol}n to the corresponding derivatives of φ{symbol} is proved. This result yields a high order approximation theorem for the input-output map generated by a nonlinear control system, using linear combinations of iterated integrals of the control.",
author = "Alberto Bressan",
year = "1984",
month = "12",
day = "1",
doi = "10.1007/BF01789393",
language = "English (US)",
volume = "137",
pages = "163--173",
journal = "Annali di Matematica Pura ed Applicata",
issn = "0373-3114",
publisher = "Springer Verlag",
number = "1",

}

High order approximation of implicitly defined maps. / Bressan, Alberto.

In: Annali di Matematica Pura ed Applicata, Vol. 137, No. 1, 01.12.1984, p. 163-173.

Research output: Contribution to journalArticle

TY - JOUR

T1 - High order approximation of implicitly defined maps

AU - Bressan, Alberto

PY - 1984/12/1

Y1 - 1984/12/1

N2 - Approximations for the function φ{symbol} implicitly defined by φ{symbol}(u)=Φ(u, φ{symbol}(u)) are obtained via the iterative scheme φ{symbol}n(u)=Φ(u, φ{symbol}n-1(u)). In this paper the uniform convergence of high order derivatives of φ{symbol}n to the corresponding derivatives of φ{symbol} is proved. This result yields a high order approximation theorem for the input-output map generated by a nonlinear control system, using linear combinations of iterated integrals of the control.

AB - Approximations for the function φ{symbol} implicitly defined by φ{symbol}(u)=Φ(u, φ{symbol}(u)) are obtained via the iterative scheme φ{symbol}n(u)=Φ(u, φ{symbol}n-1(u)). In this paper the uniform convergence of high order derivatives of φ{symbol}n to the corresponding derivatives of φ{symbol} is proved. This result yields a high order approximation theorem for the input-output map generated by a nonlinear control system, using linear combinations of iterated integrals of the control.

UR - http://www.scopus.com/inward/record.url?scp=0242673199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242673199&partnerID=8YFLogxK

U2 - 10.1007/BF01789393

DO - 10.1007/BF01789393

M3 - Article

AN - SCOPUS:0242673199

VL - 137

SP - 163

EP - 173

JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

SN - 0373-3114

IS - 1

ER -