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Introduction to geometric nonlinear control; Controllability and lie bracket

Abstract

We present an introduction to the qualitative theory of nonlinear control systems, with the main emphasis on controllability properties of such systems. We introduce the differential geometric language of vector fields, Lie bracket, distributions, foliations etc. One of the basic tools is the orbit theorem of Stefan and Sussmann. We analyse the basic controllability problems and give criteria for complete controllability, accessibility and related properties, using certain Lie algebras of ve fields defined by the system. A problem of path approximation is considered as an application of the developed theory. We illustrate our considerations with examples of simple systems or systems appearing in applications. The notes start from an elementary level and are self-contained. (author)
Authors:
Jakubczyk, B [1] 
  1. Institute of Mathematics, Polish Academy of Sciences, Warsaw (Poland)
Publication Date:
Jul 15, 2002
Product Type:
Conference
Report Number:
INIS-XA-855; LNS-028003
Resource Relation:
Conference: School on mathematical control theory, Trieste (Italy), 3-28 Sep 2001; Other Information: 8 refs, 13 figs; Related Information: In: Mathematical control theory, ICTP lecture notes CD seriesv. 8, by Agrachev, A.A. [Steklov Mathematical Institute, Moscow (Russian Federation); SISSA, Trieste (Italy)] (ed.), 774 pages.
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; CONTROL; CONTROL SYSTEMS; CONTROL THEORY; LIE GROUPS; NONLINEAR PROBLEMS; VECTOR FIELDS
OSTI ID:
20901513
Research Organizations:
Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISBN 92-95003-11-X; TRN: XA0600651063759
Availability:
Available from INIS in electronic form; Also available online: http://www.ictp.it
Submitting Site:
INIS
Size:
page(s) 108-168
Announcement Date:
Aug 28, 2007

Citation Formats

Jakubczyk, B. Introduction to geometric nonlinear control; Controllability and lie bracket. IAEA: N. p., 2002. Web.
Jakubczyk, B. Introduction to geometric nonlinear control; Controllability and lie bracket. IAEA.
Jakubczyk, B. 2002. "Introduction to geometric nonlinear control; Controllability and lie bracket." IAEA.
@misc{etde_20901513,
title = {Introduction to geometric nonlinear control; Controllability and lie bracket}
author = {Jakubczyk, B}
abstractNote = {We present an introduction to the qualitative theory of nonlinear control systems, with the main emphasis on controllability properties of such systems. We introduce the differential geometric language of vector fields, Lie bracket, distributions, foliations etc. One of the basic tools is the orbit theorem of Stefan and Sussmann. We analyse the basic controllability problems and give criteria for complete controllability, accessibility and related properties, using certain Lie algebras of ve fields defined by the system. A problem of path approximation is considered as an application of the developed theory. We illustrate our considerations with examples of simple systems or systems appearing in applications. The notes start from an elementary level and are self-contained. (author)}
place = {IAEA}
year = {2002}
month = {Jul}
}