Reduction of Nonlinear Control Systems: A Differential Geometric Approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1999
|
| Schriftenreihe: | Mathematics and Its Applications
472 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 encounters 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 approximation methods. In this monograph, we elaborate the most natural and obvious (in our opinion) approach, which is essentially inherent in any theory of mathematical 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 mathematical theory essentially begins with the introduction of these reduced objects and determination of their basic properties in relation to the initial object |
| Beschreibung: | 1 Online-Ressource (XI, 248 p) |
| ISBN: | 9789401146173 9789401059510 |
| DOI: | 10.1007/978-94-011-4617-3 |
Internformat
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| 245 | 1 | 0 | |a Reduction of Nonlinear Control Systems |b A Differential Geometric Approach |c by V. I. Elkin |
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| 500 | |a 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 encounters 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 approximation methods. In this monograph, we elaborate the most natural and obvious (in our opinion) approach, which is essentially inherent in any theory of mathematical 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 mathematical theory essentially begins with the introduction of these reduced objects and determination of their basic properties in relation to the initial object | ||
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Datensatz im Suchindex
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| isbn | 9789401146173 9789401059510 |
| language | English |
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| spelling | Elkin, V. I. Verfasser aut Reduction of Nonlinear Control Systems A Differential Geometric Approach by V. I. Elkin Dordrecht Springer Netherlands 1999 1 Online-Ressource (XI, 248 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 472 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 encounters 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 approximation methods. In this monograph, we elaborate the most natural and obvious (in our opinion) approach, which is essentially inherent in any theory of mathematical 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 mathematical theory essentially begins with the introduction of these reduced objects and determination of their basic properties in relation to the initial object Mathematics Differential Equations Systems theory Global differential geometry Mathematical optimization Systems Theory, Control Mathematics Education Calculus of Variations and Optimal Control; Optimization Ordinary Differential Equations Differential Geometry Mathematik Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Nichtlineare Kontrolltheorie (DE-588)4475218-0 s Differentialgeometrie (DE-588)4012248-7 s 1\p DE-604 Mathematics and Its Applications 472 (DE-604)BV008163334 472 https://doi.org/10.1007/978-94-011-4617-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Elkin, V. I. Reduction of Nonlinear Control Systems A Differential Geometric Approach Mathematics and Its Applications Mathematics Differential Equations Systems theory Global differential geometry Mathematical optimization Systems Theory, Control Mathematics Education Calculus of Variations and Optimal Control; Optimization Ordinary Differential Equations Differential Geometry Mathematik Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4475218-0 (DE-588)4012248-7 |
| title | Reduction of Nonlinear Control Systems A Differential Geometric Approach |
| title_auth | Reduction of Nonlinear Control Systems A Differential Geometric Approach |
| title_exact_search | Reduction of Nonlinear Control Systems A Differential Geometric Approach |
| title_full | Reduction of Nonlinear Control Systems A Differential Geometric Approach by V. I. Elkin |
| title_fullStr | Reduction of Nonlinear Control Systems A Differential Geometric Approach by V. I. Elkin |
| title_full_unstemmed | Reduction of Nonlinear Control Systems A Differential Geometric Approach by V. I. Elkin |
| title_short | Reduction of Nonlinear Control Systems |
| title_sort | reduction of nonlinear control systems a differential geometric approach |
| title_sub | A Differential Geometric Approach |
| topic | Mathematics Differential Equations Systems theory Global differential geometry Mathematical optimization Systems Theory, Control Mathematics Education Calculus of Variations and Optimal Control; Optimization Ordinary Differential Equations Differential Geometry Mathematik Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Mathematics Differential Equations Systems theory Global differential geometry Mathematical optimization Systems Theory, Control Mathematics Education Calculus of Variations and Optimal Control; Optimization Ordinary Differential Equations Differential Geometry Mathematik Nichtlineare Kontrolltheorie Differentialgeometrie |
| url | https://doi.org/10.1007/978-94-011-4617-3 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT elkinvi reductionofnonlinearcontrolsystemsadifferentialgeometricapproach |