Reduction of Nonlinear Control Systems

A Differential Geometric Approach
Softcover Nachdruck of the original 1. Auflage 1999
ISBN: 978-94-010-5951-0
Verlag: Springer Netherlands

Buch, Englisch, Band 472, 248 Seiten, Paperback, Format (B × H): 160 mm x 240 mm, Gewicht: 428 g

Reihe: Mathematics and Its Applications

Advances in science and technology necessitate the use of increasingly-complicated dynamic control processes. Undoubtedly, sophisticated mathematical models are also concurrently elaborated for these processes. In particular, linear dynamic control systems iJ = Ay + Bu, y E M C ]Rn, U E ]RT, (1) where A and B are constants, are often abandoned in favor of nonlinear dynamic control systems (2) which, in addition, contain a large number of equations. The solution of problems for multidimensional nonlinear control systems en­ counters serious difficulties, which are both mathematical and technical in nature. Therefore it is imperative to develop methods of reduction of nonlinear systems to a simpler form, for example, decomposition into systems of lesser dimension. Approaches to reduction are diverse, in particular, techniques based on approxi­ mation methods. In this monograph, we elaborate the most natural and obvious (in our opinion) approach, which is essentially inherent in any theory of math­ ematical entities, for instance, in the theory of linear spaces, theory of groups, etc. Reduction in our interpretation is based on assigning to the initial object an isomorphic object, a quotient object, and a subobject. In the theory of linear spaces, for instance, reduction consists in reducing to an isomorphic linear space, quotient space, and subspace. Strictly speaking, the exposition of any mathemat­ ical theory essentially begins with the introduction of these reduced objects and determination of their basic properties in relation to the initial object.

Zielgruppe

Research

Autoren/Hrsg.

Elkin, V. I.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Sozialwissenschaften Pädagogik Lehrerausbildung, Unterricht & Didaktik Allgemeine Didaktik

Inhaltsverzeichnis

1 Preliminaries.- 2 Categories of Control Systems.- 3 Equivalence of Control Systems.- 4 Factorization of Control Systems.- 5 Restriction of Control Systems.- 6 Certain Control Problems.