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Elkin

Reduction of Nonlinear Control Systems

A Differential Geometric Approach

Medium: Buch
ISBN: 978-0-7923-5623-3
Verlag: Springer Netherlands
Erscheinungstermin: 28.02.1999
Lieferfrist: bis zu 10 Tage

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.


Produkteigenschaften


  • Artikelnummer: 9780792356233
  • Medium: Buch
  • ISBN: 978-0-7923-5623-3
  • Verlag: Springer Netherlands
  • Erscheinungstermin: 28.02.1999
  • Sprache(n): Englisch
  • Auflage: 1999
  • Serie: Mathematics and Its Applications
  • Produktform: Gebunden
  • Gewicht: 565 g
  • Seiten: 248
  • Format (B x H x T): 160 x 241 x 19 mm
  • Ausgabetyp: Kein, Unbekannt

Themen


Autoren/Hrsg.

Autoren

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.