Mathematical control theory: deterministic finite dimensional systems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2013
|
| Ausgabe: | 2. ed., [softcover repr.] |
| Schriftenreihe: | Texts in applied mathematics
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 531 S. graph. Darst. |
| ISBN: | 1461268257 9781461268253 |
Internformat
MARC
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| 100 | 1 | |a Sontag, Eduardo D. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical control theory |b deterministic finite dimensional systems |c Eduardo D. Sontag |
| 250 | |a 2. ed., [softcover repr.] | ||
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2013 | |
| 300 | |a XVI, 531 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Texts in applied mathematics |v 6 | |
| 650 | 4 | |a Kontrolltheorie | |
| 650 | 4 | |a Systemtheorie | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a System analysis | |
| 650 | 0 | 7 | |a Systemtheorie |0 (DE-588)4058812-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kontrolltheorie |0 (DE-588)4032317-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Endliche Mathematik |0 (DE-588)4152155-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kontrolltheorie |0 (DE-588)4032317-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Systemtheorie |0 (DE-588)4058812-9 |D s |
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| 830 | 0 | |a Texts in applied mathematics |v 6 |w (DE-604)BV002476038 |9 6 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-027761339 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804152925210017792 |
|---|---|
| adam_text | Contents
Series
Preface v
Preface
to the Second
Edition
vii
Preface to the First Edition
lx
1
Introduction
і
1.1
What Is Mathematical Control Theory?
.............. 1
1.2
Proportional-Derivative Control
................... 2
1.3
Digital Control
............................ 6
1.4
Feedback Versus Precomputed Control
............... 9
1.5
State-Space and Spectrum Assignment
............... 11
1.6
Outputs and Dynamic Feedback
.................. 16
1.7
Dealing with Nonlinearity
...................... 20
1.8
A Brief Historical Background
.................... 22
1.9
Some Topics Not Covered
..................... . 23
2
Systems
25
2.1
Basic Definitions
........................... 25
2.2
I/O Behaviors
............................. 30
2.3
Discrete-Time
............................. 32
2.4
Linear Discrete Time Systems
....................
Ш
2.5
Smooth Discrete-Time Systems
................... 39
2.6
Continuous-Time
........................... 41
2.7
Linear Continuous-Time Systems
.................. 4.6
2.8
Linearizations Compute Differentials
................ 53
2.9
More on Differentiability*
...................... 64
2.10
Sampling
............................... 72
2.11
Volterra Expansions*
......................... 73
2.12
Notes and Comments
......................... 76
*Can be skipped with no loss of continuity.
ХШ
xiv Contents
3
Reachability and Controllability
81
3.1
Basic Reachability Notions
..................... 81
3.2
Time-Invariant Systems
....................... 84
3.3
Controllable Pairs of Matrices
.................... 92
3.4
Controllability Under Sampling
................... 99
3.5
More on Linear Controllability
................... 104
3.6
Bounded Controls*
.......................... 117
3.7
First-Order Local Controllability
.................. 122
3.8
Controllability of Recurrent Nets*
................. 128
3.9
Piecewise Constant Controls
..................... 136
3.10
Notes and Comments
......................... 137
4
Nonlinear Controllability
141
4.1
Lie Brackets
.............................. 141
4.2
Lie Algebras and Flows
....................... 147
4.3
Accessibility Rank Condition
.................... 154
4.4
Ad, Distributions, and Frobenius Theorem
............ 164
4.5
Necessity of Accessibility Rank Condition
............. 177
4.6
Additional Problems
......................... 179
4.7
Notes and Comments
......................... 181
5
Feedback and Stabilization
183
5.1
Constant Linear Feedback
...................... 183
5.2
Feedback Equivalence*
........................ 189
5.3
Feedback Linearization*
....................... 197
5.4
Disturbance Rejection and
Invariance*
............... 207
5.5
Stability and Other Asymptotic Notions
.............. 211
5.6
Unstable and Stable Modes*
.................... 215
5.7
Lyapunov and Control-Lyapunov Functions
............ 218
5.8
Linearization Principle for Stability
................. 233
5.9
Introduction to Nonlinear Stabilization*
.............. 239
5.10
Notes and Comments
......................... 256
6
Outputs
261
6.1
Basic Observability Notions
..................... 261
6.2
Time-Invariant Systems
....................... 268
6.3
Continuous-Time Linear Systems
.................. 276
6.4
Linearization Principle for Observability
.............. 280
6.5
Realization Theory for Linear Systems
............... 283
6.6
Recursion and Partial Realization
................. . 290
6.7
Rationality and Realizability
.................... 297
6.8
Abstract Realization Theory*
................... . 303
6.9
Notes and Comments
......................... 310
*Can be skipped with no loss of continuity.
Contents xv
7
Observers and Dynamic Feedback
315
7.1
Observers and Detectability
..................... 315
7.2
Dynamic Feedback
.......................... 321
7.3
External Stability for Linear Systems
................ 326
7.4
Frequency-Domain Considerations
................. 331
7.5
Parametrization of Stabilizers
.................... 337
7.6
Notes and Comments
......................... 344
8
Optimality: Value Function
347
8.1
Dynamic Programming*
....................... 349
8.2
Linear Systems with Quadratic Cost
................ 363
8.3
Tracking and
Kalman
Filtering*
.................. 371
8.4
Infinite-Time (Steady-State) Problem
............... 380
8.5
Nonlinear Stabilizing Optimal Controls
............... 390
8.6
Notes and Comments
......................... 394
9
Optimality; Multipliers
39У
9.1
Review of Smooth Dependence
................... 397
9.2
Unconstrained Controls
....................... 399
9.3
Excursion into the Calculus of Variations
............. 409
9.4
Gradient-Based Numerical Methods
................ 415
9.5
Constrained Controls: Minimum Principle
............. 418
9.6
Notes and Comments
......................... 421
10
Optimality: Minimum-Time for Linear Systems
423
10.1
Existence Results
........................... 424
10.2
Maximum Principle for Time-Optimality
.............. 431
10.3
Applications of the Maximum Principle
............. . 436
10.4
Remarks on the Maximum Principle
................ 443
10.5
Additional Exercises
......................... 444
10.6
Notes and Comments
......................... 446
APPENDIXES
A Linear Algebra 44V
A.I Operator Norms
........................... 447
A.
2
Singular Values
............................ 448
A.3 Jordan Forms and Matrix Functions
................ 452
A.
4
Continuity of Eigenvalues
...................... 456
В
Differentials
461
B.I Finite Dimensional Mappings
.................... 461
B.2 Maps Between Normed Spaces
................... 463
1
Can be skipped with no loss of continuity.
xvi Contents
С
Ordinary Differential
Equations
467
Cl
Review of Lebesgue Measure Theory
................467
C.2 Initial-Value Problems
........................473
C.3 Existence and Uniqueness Theorem
.................474
C.4 Linear Differential Equations
....................487
C.5 Stability of Linear Equations
....................491
Bibliography
493
List of Symbols
519
Index
523
|
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| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| edition | 2. ed., [softcover repr.] |
| format | Book |
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| indexdate | 2024-07-10T01:18:27Z |
| institution | BVB |
| isbn | 1461268257 9781461268253 |
| language | English |
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| spelling | Sontag, Eduardo D. Verfasser aut Mathematical control theory deterministic finite dimensional systems Eduardo D. Sontag 2. ed., [softcover repr.] New York, NY [u.a.] Springer 2013 XVI, 531 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 6 Kontrolltheorie Systemtheorie Control theory System analysis Systemtheorie (DE-588)4058812-9 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Endliche Mathematik (DE-588)4152155-9 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s DE-604 Systemtheorie (DE-588)4058812-9 s Endliche Mathematik (DE-588)4152155-9 s 1\p DE-604 Texts in applied mathematics 6 (DE-604)BV002476038 6 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027761339&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sontag, Eduardo D. Mathematical control theory deterministic finite dimensional systems Texts in applied mathematics Kontrolltheorie Systemtheorie Control theory System analysis Systemtheorie (DE-588)4058812-9 gnd Kontrolltheorie (DE-588)4032317-1 gnd Endliche Mathematik (DE-588)4152155-9 gnd |
| subject_GND | (DE-588)4058812-9 (DE-588)4032317-1 (DE-588)4152155-9 |
| title | Mathematical control theory deterministic finite dimensional systems |
| title_auth | Mathematical control theory deterministic finite dimensional systems |
| title_exact_search | Mathematical control theory deterministic finite dimensional systems |
| title_full | Mathematical control theory deterministic finite dimensional systems Eduardo D. Sontag |
| title_fullStr | Mathematical control theory deterministic finite dimensional systems Eduardo D. Sontag |
| title_full_unstemmed | Mathematical control theory deterministic finite dimensional systems Eduardo D. Sontag |
| title_short | Mathematical control theory |
| title_sort | mathematical control theory deterministic finite dimensional systems |
| title_sub | deterministic finite dimensional systems |
| topic | Kontrolltheorie Systemtheorie Control theory System analysis Systemtheorie (DE-588)4058812-9 gnd Kontrolltheorie (DE-588)4032317-1 gnd Endliche Mathematik (DE-588)4152155-9 gnd |
| topic_facet | Kontrolltheorie Systemtheorie Control theory System analysis Endliche Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027761339&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT sontageduardod mathematicalcontroltheorydeterministicfinitedimensionalsystems |