Global controllability and stabilization of nonlinear systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore
World Scientific
1994
|
| Series: | Series on advances in mathematics for applied sciences
20 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 270 S. graph. Darst. |
| ISBN: | 981021779X |
Staff View
MARC
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| 100 | 1 | |a Nikitin, Sergey |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Global controllability and stabilization of nonlinear systems |c S. Nikitin |
| 264 | 1 | |a Singapore |b World Scientific |c 1994 | |
| 300 | |a IX, 270 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Series on advances in mathematics for applied sciences |v 20 | |
| 650 | 7 | |a Commande automatique |2 ram | |
| 650 | 7 | |a Commande non linéaire |2 ram | |
| 650 | 7 | |a Stabilité |2 ram | |
| 650 | 7 | |a contrôlabilité |2 inriac | |
| 650 | 7 | |a géométrie différentielle |2 inriac | |
| 650 | 7 | |a stabilisation |2 inriac | |
| 650 | 7 | |a système 2D |2 inriac | |
| 650 | 7 | |a système multidimensionnel |2 inriac | |
| 650 | 7 | |a système non linéaire |2 inriac | |
| 650 | 4 | |a Automatic control | |
| 650 | 4 | |a Nonlinear control theory | |
| 650 | 4 | |a Stability | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-006854912 | ||
Record in the Search Index
| _version_ | 1804124720814096384 |
|---|---|
| adam_text | vii
Contents
Preface v
I Two dimensional affine nonlinear systems 1
1 Controllability of cart 3
1.1 Prisons and mysteries of a plain domain 3
1.2 Controllability criteria for linear systems under
phase constraints 7
1.3 Controllability analysis in a convex domain 21
1.4 How do control constraints change life? 25
1.5 Exercises 32
2 Nonlinear affine system on a plane as a cart garland 35
2.1 About one nonlinear system which is equivalent to a cart . . 35
2.2 Controllability of a cart garland 41
2.3 Affine nonlinear system with control constraints 50
2.4 Dynamic of populations under external influence 58
2.5 Exercises 65
3 Semiglobal stabilization of cart garland 69
3.1 Stabilization of a system being equivalent to a cart 69
3.2 Stable covering and semiglobal stabilization 74
3.3 Some examples of adaptive stabilizers 80
3.3.1 Sliding stabilizer 81
3.3.2 High gain adaptive stabilizer 83
3.4 A simplified auto pilot system and tracking control
problem of robotic manipulators 87
3.4.1 A simplified auto pilot system 87
3.4.2 Tracking control problem of robotic manipulators . . 90
3.4.3 Exercises 93
4 Two dimensional systems with singularities 97
4.1 Normal forms of systems with singularities 97
4.2 Controllability and stabilization of systems with
singularities 103
4.2.1 Controllability of systems with singularities .... 103
4.2.2 Local stabilization at a singularity of type I .... 113
viii
4.3 Classification of singularities, controllability criteria of
bilinear systems on a plane 120
4.3.1 Classification of bilinear systems 121
4.3.2 Controllability criteria 127
4.4 Exercises 143
II Multi dimensional nonlinear systems 147
1 Global controllability analysis 149
1.1 A brief review of basic concepts of topology and
differential geometry 149
1.1.1 Topological spaces 150
1.1.2 Smooth manifolds 153
1.1.3 Tangent bundle and vector fields 157
1.2 Groups and monoids 164
1.3 Approximative groups and systems on foliations 166
1.3.1 Approximative groups 166
1.3.2 System on foliations 181
1.4 Necessary and sufficient conditions of global controllability 186
1.4.1 When does the existence of transitive approximative
group imply controllability? 186
1.4.2 Full rank conditions of global controllability .... 190
1.4.3 Systems on foliations and controllability of
nonlinear systems 197
1.5 Hypersurface systems 203
1.6 Exercises 210
2 Local stabilization of nonlinear systems 213
2.1 The simplest necessary and sufficient conditions of
local stabilization 213
2.2 Liapunov s direct method 220
2.2.1 Sontag s formula of almost smooth stabilizer .... 221
2.2.2 Jurdjevic Quinn approach 222
2.2.3 Stabilization of homogeneous systems 223
2.3 Decoupling normalizing transformations and local
stabilization of nonlinear systems 226
2.3.1 Existence of decoupling normalizing transformations 226
ix
2.3.2 Local stabilization of nonlinear systems and
approximation of decoupling normalizing
transformations 239
2.4 Exercises 247
3 Semiglobal stabilization 251
3.1 Necessary conditions of smooth stabilization in the large . 251
3.1.1 Some facts about degree of function 252
3.1.2 Multi input systems 256
3.1.3 Single input systems 257
3.2 The relationship between controllability and stabilization . 259
3.3 Exercises 265
References 267
|
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| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003.75 |
| dewey-search | 003.75 |
| dewey-sort | 13.75 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
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| id | DE-604.BV010302625 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:50:09Z |
| institution | BVB |
| isbn | 981021779X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006854912 |
| oclc_num | 31764225 |
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| owner | DE-29T DE-703 |
| owner_facet | DE-29T DE-703 |
| physical | IX, 270 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on advances in mathematics for applied sciences |
| series2 | Series on advances in mathematics for applied sciences |
| spelling | Nikitin, Sergey Verfasser aut Global controllability and stabilization of nonlinear systems S. Nikitin Singapore World Scientific 1994 IX, 270 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on advances in mathematics for applied sciences 20 Commande automatique ram Commande non linéaire ram Stabilité ram contrôlabilité inriac géométrie différentielle inriac stabilisation inriac système 2D inriac système multidimensionnel inriac système non linéaire inriac Automatic control Nonlinear control theory Stability Nichtlineares System (DE-588)4042110-7 gnd rswk-swf Stabilisierung (DE-588)4357300-9 gnd rswk-swf Nichtlineares System (DE-588)4042110-7 s Stabilisierung (DE-588)4357300-9 s DE-604 Series on advances in mathematics for applied sciences 20 (DE-604)BV004569239 20 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006854912&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nikitin, Sergey Global controllability and stabilization of nonlinear systems Series on advances in mathematics for applied sciences Commande automatique ram Commande non linéaire ram Stabilité ram contrôlabilité inriac géométrie différentielle inriac stabilisation inriac système 2D inriac système multidimensionnel inriac système non linéaire inriac Automatic control Nonlinear control theory Stability Nichtlineares System (DE-588)4042110-7 gnd Stabilisierung (DE-588)4357300-9 gnd |
| subject_GND | (DE-588)4042110-7 (DE-588)4357300-9 |
| title | Global controllability and stabilization of nonlinear systems |
| title_auth | Global controllability and stabilization of nonlinear systems |
| title_exact_search | Global controllability and stabilization of nonlinear systems |
| title_full | Global controllability and stabilization of nonlinear systems S. Nikitin |
| title_fullStr | Global controllability and stabilization of nonlinear systems S. Nikitin |
| title_full_unstemmed | Global controllability and stabilization of nonlinear systems S. Nikitin |
| title_short | Global controllability and stabilization of nonlinear systems |
| title_sort | global controllability and stabilization of nonlinear systems |
| topic | Commande automatique ram Commande non linéaire ram Stabilité ram contrôlabilité inriac géométrie différentielle inriac stabilisation inriac système 2D inriac système multidimensionnel inriac système non linéaire inriac Automatic control Nonlinear control theory Stability Nichtlineares System (DE-588)4042110-7 gnd Stabilisierung (DE-588)4357300-9 gnd |
| topic_facet | Commande automatique Commande non linéaire Stabilité contrôlabilité géométrie différentielle stabilisation système 2D système multidimensionnel système non linéaire Automatic control Nonlinear control theory Stability Nichtlineares System Stabilisierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006854912&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004569239 |
| work_keys_str_mv | AT nikitinsergey globalcontrollabilityandstabilizationofnonlinearsystems |