Constructive nonlinear control:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
London [u.a.]
Springer
2012
|
| Ausgabe: | [softcover repr. of the harcover 1. ed. 1997] |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027725786&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027725786&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 313 S. Ill., graph. Darst. |
Internformat
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| 245 | 1 | 0 | |a Constructive nonlinear control |c R. Sepulchre ; M. Jankovi'c and P. V. Kokotovi'c |
| 250 | |a [softcover repr. of the harcover 1. ed. 1997] | ||
| 264 | 1 | |a London [u.a.] |b Springer |c 2012 | |
| 300 | |a XI, 313 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 0 | 7 | |a Nichtlineares Regelungssystem |0 (DE-588)4276212-1 |2 gnd |9 rswk-swf |
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| 689 | 0 | 0 | |a Nichtlineares Regelungssystem |0 (DE-588)4276212-1 |D s |
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| 700 | 1 | |a Janković, Mrdjan |e Verfasser |4 aut | |
| 700 | 1 | |a Kokotović, Petar V. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1819324284631252992 |
|---|---|
| adam_text | Constructive
Nonlinear
Control
presents a broad repertoire of
constructive nonlinear designs not available in other works by
widening the class of systems and design tools.
This innovative work includes the following:
•
Several streams of nonlinear control theory are merged and
directed towards a constructive solution of the feedback
stabilization problem.
•
Analysis, geometric and asymptotic concepts are assembled
as design tools for a wide variety of nonlinear phenomena
and structures.
•
Geometry serves as a guide for the construction of design
procedures whilst analysis provides the robustness which
geometry lacks.
•
New recursive designs remove earlier restrictions on
feedback passivation.
•
Recursive Lyapunov designs for feedback, feedforward and
interlaced structures result in feedback systems with
optimality properties and stability margins.
•
Basic concepts are illustrated by examples and design
applications on several physical models of practical interest.
The design-oriented approach of this work will make it an
invaluable tool for control engineers, graduate students and
applied mathematicians who have an interest in control theory.
The Communications and Control Engineering Series reflects
major technological advances which have a great impact in the
fields of communication and control. It reports on the research
in industrial and academic institutions around the world to
exploit the new possibilities which are becoming available.
Contents
Introduction
1
1.1
Passivity, Optimality, and Stability
2
1.1.1
From absolute stability to passivity
2
1.1.2
Passivity as a phase characteristic
3
1.1.3
Optimal control and stability margins
5
1.2
Feedback Passivation
6
1.2.1
Limitations of feedback linearization
б
1.2.2
Feedback passivation and forwarding
7
1.3
Cascade Designs
8
1.3.1
Passivation with composite Lyapunov functions
8
1.3.2
A structural obstacle: peaking
9
1.4
Lyapunov Constructions
12
1.4.1
Construction of the cross-term
12
1.4.2
A benchmark example
13
1.4.3
Adaptive control
lõ
l.o Recursive Designs
15
1.5.1
Obstacles to passivation
15
1.5.2
Removing the relative degree obstacle
16
1.5.3
Removing the minimum phase obstacle IV
1.5.4
System, structures
18
1.5.5
Approximate asymptotic designs
19
1.6
Book Style and Notation
23
1.6.1
Styie
23
1.6.2
Notation and acronyms
23
viii Contents
2
Passivity Concepts as Design Tools
25
2.1
Dissipativity and Passivity
26
2.1.1
Classes of systems
26
2.1.2
Basic concepts
27
2.2
Interconnections of Passive Systems
31
2.2.1
Parallel and feedback interconnections
31
2.2.2
Excess and shortage of passivity
34
2.3
Lyapunov Stability and Passivity
40
2.3.1
Stability and convergence theorems
40
2.3.2
Stability with
semidefinite
Lyapunov functions
45
2.3.3
Stability of passive systems
48
2.3.4
Stability of feedback interconnections
50
2.3.5
Absolute stability
54
2.3.6
Characterization of
affine
dissipative systems
56
2.4
Feedback Passivity
59
2.4.1
Passivity: a tool for stabilization
59
2.4.2
Feedback passive linear systems
60
2.4.3
Feedback passive nonlinear systems
63
2.4.4
Output feedback passivity
66
2.5
Summary
68
2.6
Notes and References
68
3
Stability Margins and Optimality
71
3.1
Stability Margins for Linear Systems
72
3.1.1
Classical gain and phase margins
72
3.1.2
Sector and disk margins
75
3.1.3
Disk margin and output feedback passivity
78
3.2
Input Uncertainties
83
3.2.1
Static and dynamic uncertainties
83
3.2.2
Stability margins for nonlinear feedback systems
86
3.2.3
Stability with fast unmodeled dynamics
86
3.3
Optimality, Stability, and Passivity
91
3.3.1
Optimal stabilizing control
91
3.3.2
Optimality and passivity
95
3.4
Stability Margins of Optimal Systems
99
3.4.1
Disk margin for R(x)
- ƒ 99
Contents ix
3.4.2
Sector
margin
for diagonal R{x)
φ
I
100
3.4.3
Achieving a disk margin by domination
103
3.5
Inverse Optimal Design
107
3.5.1
inverse optimality
107
3.5.2
Damping control for stable systems
110
3.5.3
CLF for inverse optimal control
112
3.6
Summary
119
3.7
Notes and References
120
4
Cascade Designs
123
4.1
Cascade Systems
124
4.1.1 TORA
system
124
4.1.2
Types of cascades
125
4.2
Partial· State Feedback Designs
126
4.2.1
Local stabilization
126
4.2.2
Growth restrictions for global stabilization
128
4.2.3
ISS condition for global stabilization
133
4.2.4
Stability margins: partial-state feedback
135
4.3
Feedback Passivation of Cascades
138
4.4
Designs for the
TORA
System
145
4.4.1 TORA
models
145
4.4.2
Two preliminary designs 14G
4.4.3
Controllers with gain margin
148
4.4.4
A redesign to improve performance
149
4.5
Output Peaking: an Obstacle to Global Stabilization
153
4.5.1
The peaking phenomenon
153
4.5.2
Nonpeaking linear systems
157
4.5.3
Peaking and
semiglobal
stabilization of cascades
163
4.6
Summary
170
4.7
Notes and References
171
5
Construction of Lyapunov functions
1Ϋ3
5.1
Composite Lyapunov functions for cascade systems
174
5.1.1
Benchmark system
174
5.1.2
Cascade structure
176
5.1.3
Composite Lyapunov functions
178
5.2
Lyapunov Construction with a Cross-Term
183
x
Contents
5.2.1
The construction of the cross-term
183
5.2.2
Differentiability of the function
Φ
188
5.2.3
Computing the cross-term
194
5.3
Relaxed Constructions
198
5.3.1
Geometric interpretation of the cross-term
198
5.3.2
Relaxed change of coordinates
201
5.3.3
Lvapunov functions with relaxed cross-term
203
5.4
Stabilization of Augmented Cascades
208
5.4.1
Design of the stabilizing feedback laws
208
5.4.2
A structural condition for GAS and
LES
210
5.4.3
Ball-and-beam example
214
5.5
Lvapunov functions for adaptive control
216
5.5.1
Parametric Lyapunov Functions
217
5.5.2
Control with known
θ
219
5.5.3
Adaptive Controller Design
221
5.6
Summary
226
5.7
Notes and references
227
6
Recursive designs
229
6.1
Backstepping
230
6.1.1
Introductory example
230
6.1.2
Backstepping procedure
235
6.1.3
Nested high-gain designs
239
6.2
Forwarding
249
6.2.1
Introductory example
249
6.2.2
Forwarding procedure
253
6.2.3
Removing the weak minimum phase obstacle
257
6.2.4
Geometric properties of forwarding
263
6.2.5
Designs with saturation
266
6.2.6
Trade-offs in saturation designs
273
6.3
Interlaced Systems
276
6.3.1
Introductory example
276
6.3.2
Non-affine systems
278
6.3.3
Structural conditions for global stabilization
280
6.4
Summary and Perspectives
283
6.5
Notes and References
284
Contents
χι
A Basic geometric concepts
285
A.I Relative Degree
285
A.
2
Normal Form
28?
A.3 The Zero Dynamics
290
A.
4
Right-invertibility >g->
A.
5
Geometric properties
293
В
Proofs of Theorems
3.18
and
4,35 295
В
. 1
Proof of Theorem
3.18 295
B.2 Proof of Theorem
4.35 297
Bibliography 301
Index 311
|
| any_adam_object | 1 |
| author | Sepulchre, Rodolphe Janković, Mrdjan Kokotović, Petar V. |
| author_facet | Sepulchre, Rodolphe Janković, Mrdjan Kokotović, Petar V. |
| author_role | aut aut aut |
| author_sort | Sepulchre, Rodolphe |
| author_variant | r s rs m j mj p v k pv pvk |
| building | Verbundindex |
| bvnumber | BV042288569 |
| classification_rvk | SK 880 |
| ctrlnum | (OCoLC)902664398 (DE-599)BVBBV042288569 |
| discipline | Mathematik |
| edition | [softcover repr. of the harcover 1. ed. 1997] |
| format | Book |
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| id | DE-604.BV042288569 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T17:06:52Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027725786 |
| oclc_num | 902664398 |
| open_access_boolean | |
| owner | DE-739 |
| owner_facet | DE-739 |
| physical | XI, 313 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Sepulchre, Rodolphe Janković, Mrdjan Kokotović, Petar V. Constructive nonlinear control Nichtlineares Regelungssystem (DE-588)4276212-1 gnd Ljapunov-Funktion (DE-588)4274502-0 gnd Rückkopplung (DE-588)4050851-1 gnd |
| subject_GND | (DE-588)4276212-1 (DE-588)4274502-0 (DE-588)4050851-1 |
| title | Constructive nonlinear control |
| title_auth | Constructive nonlinear control |
| title_exact_search | Constructive nonlinear control |
| title_full | Constructive nonlinear control R. Sepulchre ; M. Jankovi'c and P. V. Kokotovi'c |
| title_fullStr | Constructive nonlinear control R. Sepulchre ; M. Jankovi'c and P. V. Kokotovi'c |
| title_full_unstemmed | Constructive nonlinear control R. Sepulchre ; M. Jankovi'c and P. V. Kokotovi'c |
| title_short | Constructive nonlinear control |
| title_sort | constructive nonlinear control |
| topic | Nichtlineares Regelungssystem (DE-588)4276212-1 gnd Ljapunov-Funktion (DE-588)4274502-0 gnd Rückkopplung (DE-588)4050851-1 gnd |
| topic_facet | Nichtlineares Regelungssystem Ljapunov-Funktion Rückkopplung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027725786&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027725786&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sepulchrerodolphe constructivenonlinearcontrol AT jankovicmrdjan constructivenonlinearcontrol AT kokotovicpetarv constructivenonlinearcontrol |