| Reduction of Nonlinear Control Systems: A Differential Geometric Approach 1999 Edition Contributor(s): Elkin, V. I. (Author) |
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ISBN: 0792356233 ISBN-13: 9780792356233 Publisher: Springer OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: February 1999 |
| Additional Information |
| BISAC Categories: - Technology & Engineering | Robotics - Mathematics - Medical |
| Dewey: 629.831 |
| LCCN: 99199840 |
| Series: Mathematics and Its Applications |
| Physical Information: 0.63" H x 6.14" W x 9.21" (1.20 lbs) 248 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |
