Nonlinear and optimal control theory: lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19 - 29, 2004
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| Other Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Series: | Lecture notes in mathematics
1932 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 351 S. graph. Darst. |
| ISBN: | 9783540776444 3540776443 |
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| 245 | 1 | 0 | |a Nonlinear and optimal control theory |b lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19 - 29, 2004 |c Andrei A. Agrachev ... Ed.: Paolo Nistri ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XIII, 351 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1932 | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Nonlinear control theory | |
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| 700 | 1 | |a Agračev, Andreij A. |4 ctb | |
| 700 | 1 | |a Nistri, Paolo |4 edt | |
| 710 | 2 | |a Centro Internazionale Matematico Estivo |e Sonstige |0 (DE-588)1025933-8 |4 oth | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Geometry
of Optimal Control Problems and Hamiltonian
Systems
A.A.
Agrachev
................................................... 1
1 Lagrange
Multipliers Geometry
................................. 1
1.1
Smooth Optimal Control Problems
.......................... 1
1.2 Lagrange
Multipliers
....................................... 4
1.3
Extremals
................................................ 6
1.4
Hamiltonian System
....................................... 7
1.5
Second Order Information
.................................. 10
1.6
Maslov Index
............................................. 14
1.7
Regular Extremals
........................................ 22
2
Geometry of Jacobi Curves
..................................... 25
2.1
Jacobi Curves
............................................. 25
2.2
The Cross-Ratio
.......................................... 26
2.3
Coordinate Setting
........................................ 28
2.4
Curves in the Grassmannian
................................ 29
2.5
The Curvature
............................................ 30
2.6
Structural Equations
....................................... 33
2.7
Canonical Connection
...................................... 35
2.8
Coordinate Presentation
................................... 38
2.9 Affine
Foliations
........................................... 39
2.10
Symplectic Setting
........................................ 41
2.11
Monotonicity
............................................. 44
2.12
Comparison Theorem
...................................... 49
2.13
Reduction
................................................ 51
2.14
Hyperbolicity
............................................. 53
References
...................................................... 58
Lecture Notes on Logically Switched Dynamical Systems
A.S. Morse
...................................................... 61
1
The Quintessential Switched Dynamical System Problem
........... 62
1.1
Dwell-Time Switching
...................................... 62
XII Contents
2
Preliminaries and Background
..................................222
2.1
Review of Some Notational Conventions and Definitions
........222
2.2
Generalized Jacobians,
Derivate
Containers, and Michel-Penot
Subdifferentials
...........................................228
2.3
Finitely Additive Measures
.................................229
3
Cellina Continuously Approximable Maps
........................230
3.1
Definition and Elementary Properties
........................231
3.2
Fixed Point Theorems for CCA Maps
........................234
4
GDQs and AGDQs
............................................243
4.1
The Basic Definitions
......................................244
4.2
Properties of GDQs and AGDQs
............................246
4.3
The Directional Open Mapping and Transversality Properties
... 255
5
Variational Generators
.........................................267
5.1
Linearization Error and Weak GDQs
........................267
5.2
GDQ Variational Generators
................................269
5.3
Examples of Variational Generators
..........................270
6
Discontinuous Vector Fields
.....................................277
6.1
Co-Integrably Bounded Integrally Continuous Maps
...........277
6.2
Points of Approximate Continuity
...........................280
7
The Maximum Principle
........................................281
References
......................................................285
Sliding Mode Control: Mathematical Tools, Design
and Applications
V.l.
Utkin
......................................................289
1
Introduction
..................................................289
2
Examples of Dynamic Systems with Sliding Modes
................289
3
VSS
in Canonical Space
.......................................296
3.1
Control of Free Motion
.....................................298
3.2
Disturbance Rejection
.....................................300
3.3
Comments for
VSS
in Canonical Space
.......................301
3.4
Preliminary Mathematical Remark
..........................302
4
Sliding Modes in Arbitrary State Spaces: Problem Statements
.......303
5
Sliding Mode Equations: Equivalent Control Method
...............305
5.1
Problem Statement
........................................305
5.2
Regularization
............................................306
5.3
Boundary Layer Regularization
.............................311
6
Sliding Mode Existence Conditions
..............................313
7
Design Principles
..............................................316
7.1
Decoupling and
Invariance
..................................316
7.2
Regular Form
.............................................318
7.3
Block Control Principle
....................................320
7.4
Enforcing Sliding Modes
...................................322
7.5
Unit Control
..............................................325
8
The Chattering Problem
.......................................327
Contents XIII
9
Discrete-Time Systems
.........................................330
9.1
Discrete-Time Sliding Mode Concept
........................331
9.2
Linear Discrete-Time Systems with Known Parameters
.........333
9.3
Linear Discrete-Time Systems with Unknown Parameters
......335
10
Infinite-Dimensional Systems
...................................336
10.1
Distributed Control of Heat Process
.........................337
10.2
Flexible Mechanical System
.................................338
11
Control of Induction Motor
....................................340
References
......................................................344
List of Participants
............................................349
|
| adam_txt |
Contents
Geometry
of Optimal Control Problems and Hamiltonian
Systems
A.A.
Agrachev
. 1
1 Lagrange
Multipliers' Geometry
. 1
1.1
Smooth Optimal Control Problems
. 1
1.2 Lagrange
Multipliers
. 4
1.3
Extremals
. 6
1.4
Hamiltonian System
. 7
1.5
Second Order Information
. 10
1.6
Maslov Index
. 14
1.7
Regular Extremals
. 22
2
Geometry of Jacobi Curves
. 25
2.1
Jacobi Curves
. 25
2.2
The Cross-Ratio
. 26
2.3
Coordinate Setting
. 28
2.4
Curves in the Grassmannian
. 29
2.5
The Curvature
. 30
2.6
Structural Equations
. 33
2.7
Canonical Connection
. 35
2.8
Coordinate Presentation
. 38
2.9 Affine
Foliations
. 39
2.10
Symplectic Setting
. 41
2.11
Monotonicity
. 44
2.12
Comparison Theorem
. 49
2.13
Reduction
. 51
2.14
Hyperbolicity
. 53
References
. 58
Lecture Notes on Logically Switched Dynamical Systems
A.S. Morse
. 61
1
The Quintessential Switched Dynamical System Problem
. 62
1.1
Dwell-Time Switching
. 62
XII Contents
2
Preliminaries and Background
.222
2.1
Review of Some Notational Conventions and Definitions
.222
2.2
Generalized Jacobians,
Derivate
Containers, and Michel-Penot
Subdifferentials
.228
2.3
Finitely Additive Measures
.229
3
Cellina Continuously Approximable Maps
.230
3.1
Definition and Elementary Properties
.231
3.2
Fixed Point Theorems for CCA Maps
.234
4
GDQs and AGDQs
.243
4.1
The Basic Definitions
.244
4.2
Properties of GDQs and AGDQs
.246
4.3
The Directional Open Mapping and Transversality Properties
. 255
5
Variational Generators
.267
5.1
Linearization Error and Weak GDQs
.267
5.2
GDQ Variational Generators
.269
5.3
Examples of Variational Generators
.270
6
Discontinuous Vector Fields
.277
6.1
Co-Integrably Bounded Integrally Continuous Maps
.277
6.2
Points of Approximate Continuity
.280
7
The Maximum Principle
.281
References
.285
Sliding Mode Control: Mathematical Tools, Design
and Applications
V.l.
Utkin
.289
1
Introduction
.289
2
Examples of Dynamic Systems with Sliding Modes
.289
3
VSS
in Canonical Space
.296
3.1
Control of Free Motion
.298
3.2
Disturbance Rejection
.300
3.3
Comments for
VSS
in Canonical Space
.301
3.4
Preliminary Mathematical Remark
.302
4
Sliding Modes in Arbitrary State Spaces: Problem Statements
.303
5
Sliding Mode Equations: Equivalent Control Method
.305
5.1
Problem Statement
.305
5.2
Regularization
.306
5.3
Boundary Layer Regularization
.311
6
Sliding Mode Existence Conditions
.313
7
Design Principles
.316
7.1
Decoupling and
Invariance
.316
7.2
Regular Form
.318
7.3
Block Control Principle
.320
7.4
Enforcing Sliding Modes
.322
7.5
Unit Control
.325
8
The Chattering Problem
.327
Contents XIII
9
Discrete-Time Systems
.330
9.1
Discrete-Time Sliding Mode Concept
.331
9.2
Linear Discrete-Time Systems with Known Parameters
.333
9.3
Linear Discrete-Time Systems with Unknown Parameters
.335
10
Infinite-Dimensional Systems
.336
10.1
Distributed Control of Heat Process
.337
10.2
Flexible Mechanical System
.338
11
Control of Induction Motor
.340
References
.344
List of Participants
.349 |
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| id | DE-604.BV023244521 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:25:10Z |
| indexdate | 2024-07-09T21:13:59Z |
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| isbn | 9783540776444 3540776443 |
| language | English |
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| physical | XIII, 351 S. graph. Darst. |
| publishDate | 2008 |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Nonlinear and optimal control theory lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19 - 29, 2004 Andrei A. Agrachev ... Ed.: Paolo Nistri ... Berlin [u.a.] Springer 2008 XIII, 351 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1932 Mathematical optimization Nonlinear control theory Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2004 Cetraro gnd-content Kontrolltheorie (DE-588)4032317-1 s DE-604 Agračev, Andreij A. ctb Nistri, Paolo edt Centro Internazionale Matematico Estivo Sonstige (DE-588)1025933-8 oth Lecture notes in mathematics 1932 (DE-604)BV000676446 1932 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016430005&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nonlinear and optimal control theory lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19 - 29, 2004 Lecture notes in mathematics Mathematical optimization Nonlinear control theory Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)1071861417 |
| title | Nonlinear and optimal control theory lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19 - 29, 2004 |
| title_auth | Nonlinear and optimal control theory lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19 - 29, 2004 |
| title_exact_search | Nonlinear and optimal control theory lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19 - 29, 2004 |
| title_exact_search_txtP | Nonlinear and optimal control theory lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19 - 29, 2004 |
| title_full | Nonlinear and optimal control theory lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19 - 29, 2004 Andrei A. Agrachev ... Ed.: Paolo Nistri ... |
| title_fullStr | Nonlinear and optimal control theory lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19 - 29, 2004 Andrei A. Agrachev ... Ed.: Paolo Nistri ... |
| title_full_unstemmed | Nonlinear and optimal control theory lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19 - 29, 2004 Andrei A. Agrachev ... Ed.: Paolo Nistri ... |
| title_short | Nonlinear and optimal control theory |
| title_sort | nonlinear and optimal control theory lectures given at the c i m e summer school held in cetraro italy june 19 29 2004 |
| title_sub | lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19 - 29, 2004 |
| topic | Mathematical optimization Nonlinear control theory Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Mathematical optimization Nonlinear control theory Kontrolltheorie Konferenzschrift 2004 Cetraro |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016430005&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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