Reduction of Nonlinear Control Systems

A Differential Geometric Approach

  • V. I. Elkin

Part of the Mathematics and Its Applications book series (MAIA, volume 472)

Table of contents

  1. Front Matter
    Pages i-xi
  2. V. I. Elkin
    Pages 1-106
  3. V. I. Elkin
    Pages 107-115
  4. V. I. Elkin
    Pages 116-159
  5. V. I. Elkin
    Pages 160-186
  6. V. I. Elkin
    Pages 187-216
  7. V. I. Elkin
    Pages 217-242
  8. Back Matter
    Pages 243-248

About this book

Introduction

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.

Keywords

Immersion control control system nonlinear control

Authors and affiliations

  • V. I. Elkin
    • 1
    • 2
  1. 1.Computing Centre of the Russian Academy of SciencesMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-011-4617-3
  • Copyright Information Springer Science+Business Media B.V. 1999
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-5951-0
  • Online ISBN 978-94-011-4617-3
  • About this book
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