Multi-resolution methods for modeling and control of dynamical systems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press, Taylor & Francis
2009
|
| Series: | Chapman & Hall/CRC applied mathematics and nonlinear science series
16 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 285 - 295 |
| Physical Description: | XVI, 299 S. Ill., graph. Darst. |
| ISBN: | 9781584887690 |
Staff View
MARC
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| 245 | 1 | 0 | |a Multi-resolution methods for modeling and control of dynamical systems |c Puneet Singla ; John L. Junkins |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b CRC Press, Taylor & Francis |c 2009 | |
| 300 | |a XVI, 299 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Chapman & Hall/CRC applied mathematics and nonlinear science series |v 16 | |
| 500 | |a Literaturverz. S. 285 - 295 | ||
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| 650 | 4 | |a Mathematisches Modell | |
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Record in the Search Index
| _version_ | 1804138123372789760 |
|---|---|
| adam_text | Contents
Least
Squares
Methods
1
1.1
Introduction
............................ 1
1.2
The Least Squares Algorithm
.................. 2
1.3
Linear Least Squares Methods
.................. 3
1.3.1
Batch Least Squares Method
.............. 3
1.3.2
Sequential Least Squares Algorithm
.......... 5
1.4
Non-Linear Least Squares Algorithm
.............. 8
1.5
Properties of Least Squares Algorithms
............. 10
1.6
Examples
............................. 11
1.6.1
Smooth Function Approximation
............ 11
1.6.2
Star Camera Calibration
................. 12
1.7
Summary
............................. 19
Polynomial Approximation
21
2.1
Introduction
............................ 21
2.2
Gram-Schmidt Procedure of Orthogonalization
........ 22
2.2.1
Three-Term Recurrence Relation to Generate
Orthogonal Polynomials
................. 24
2.2.2
Uniqueness of Orthogonal Polynomials
......... 25
2.3
Hypergeometric Function Approach to Generate Orthogonal
Polynomials
............................ 30
2.3.1
Derivation of Rodrigues s Formula for Continuous
Variable Polynomials
................... 34
2.3.2
Leading Coefficients for Three-Term Recurrence
Formula
.......................... 36
2.4
Discrete Variable Orthogonal Polynomials
........... 38
2.4.1
Hypergeometric Type Difference Equation
....... 39
2.4.2
Derivation of Rodrigues s Formula for Discrete
Variable Orthogonal Polynomials
............ 42
2.4.3
Leading Coefficients for Three-Term Recurrence
Formula for Discrete Variable Orthogonal
Polynomials
........................ 44
2.5
Approximation Properties of Orthogonal Polynomials
.... 45
2.6
Summary
............................. 48
vu
Vlil
3
Artificial
Neural
Networks
for Input-Output Approximation
49
3.1
Introduction
............................ 49
3.1.1
Radial Basis Function Networks
............. 50
3.2
Direction-Dependent Approach
................. 55
3.3
Directed Connectivity Graph
.................. 60
3.3.1
Estimation Algorithm
.................. 62
3.3.2
Spectral Decomposition of the Covariance Matrix
. . 64
3.3.3
Additive Decomposition of the Covariance Matrix
. . 66
3.3.4
Cholesky Decomposition of the
Сол^агіапсе
Matrix
. . 66
3.4
Modified Minimal Resource Allocating Algorithm
(MMRAN)
............................ 69
3.5
Numerical Simulation Examples
................. 72
3.5.1
Test Example
1:
Function Approximation
....... 73
3.5.2
Test Example
2:
3-Input 1-Output Continuous
Function Approximation
................. 80
3.5.3
Test Example
3:
Dynamical System Identification
... 82
3.5.4
Test Example
4:
Chaotic Time Series Prediction
... 86
3.5.5
Test Example
5:
Benchmark Against the On-Line
Structural Adaptive Hybrid Learning (OXSAHL)
Algorithm
......................... 90
3.6
Summary
............................. 93
4
Multi-Resolution Approximation Methods
95
4.1
Introduction
............................ 95
4.2
Wavelets
.............................. 97
4.3
Bèzier
Spline
........................... 105
4.4
Moving Least Squares Method
................. 110
4.5
Adaptive Multi-Resolution Algorithm
............. 112
4.6
Numerical Results
........................ 116
4.6.1
Calibration of Vision Sensors
.............. 116
4.6.2
Simulation and Results
.................. 117
4.6.3
DCG Approximation Result
............... 119
4.6.4
Local Approximation Results
.............. 121
4.7
Summan·
............................. 121
5
Global Local Orthogonal Polynomial MAPping (GLO-MAP)
in
N
Dimensions
123
5.1
Introduction
............................123
5.2
Basic Ideas
............................
125
5.3
Approximation in
1. 2
and
N
Dimensions Using Weighting
Functions
.............................128
5.4
Global-Local Orthogonal Approximation in
1-, 2-
and
.Y-Dimensional Spaces
......................136
5.4.1
1-Dimensional Case
....................139
■5.4.2
2-Dimensional Case
....................140
їх
5.4.3
^-Dimensional Case
...................142
5.5
Algorithm Implementation
....................144
5.5.1
Sequential Version of the GLO-MAP Algorithm
.... 146
5.6
Properties of GLO-MAP Approximation
............149
5.6.1
Approximation Error
...................149
5.6.2
Bounds on Approximation Error
............150
5.6.3
Probabilistic Analysis of the GLO-MAP Algorithm
. . 152
5.7
Illustrative Engineering Applications
..............155
5.7.1
Function Approximation
................. 155
5.7.2
Synthetic Jet Actuator Modeling
............ 160
5.7.3
Space-Based Radar (SBR) Antenna Shape
Approximation
...................... 166
5.7.4
Porkchop Plot Approximations for Mission to
Near-Earth Objects (NEOs)
............... 170
5.8
Summary
............................. 174
Nonlinear System Identification
179
6.1
Introduction
............................179
6.2
Problem Statement and Background
..............180
6.3
Novel System Identification Algorithm
.............182
6.3.1
Linear System Identification
...............185
6.3.2
State Variable Estimation
................189
6.4
Nonlinear System Identification Algorithm
...........190
6.4.1
Learning Algorithm for State Model Perturbation
Approach (SysID
1) ...................190
6.4.2
Learning Algorithm for Output Model Perturbation
Approach (SysID
2) ...................197
6.5
Numerical Simulation
......................199
6.5.1
Dynamic System Identification of Large Space
Antenna
..........................199
6.6
Summary
.............................205
Distributed Parameter Systems
207
7.1
Introduction
............................ 207
7.2
MLPG-Moving Least Squares Approach
............ 210
7.2.1
Poisson
Equation
..................... 214
7.2.2
Comments on the MLPG Algorithm
.......... 220
7.3
Partition of Unity Finite Element Method
........... 222
7.3.1
Poisson
Equation
..................... 228
7.3.2
Fokker-Planck-Kolmogorov Equation
.......... 235
7.4
Summary
............................. 240
8
Control
Distribution
for Over-Actuated Systems
243
8.1
Introduction
............................243
8.2
Problem Statement and Background
..............245
8.3
Control Distribution Functions
.................251
8.3.1
Radial Basis Functions
..................254
8.3.2
Global Local Orthogonal Basis Functions
.......255
8.4
Hierarchical Control Distribution Algorithm
..........259
8.5
Numerical Results
........................264
8.5.1
Control Allocation for a Morphing Wing
........264
8.6
Summary
.............................273
Appendix
275
References
285
Index
297
|
| adam_txt |
Contents
Least
Squares
Methods
1
1.1
Introduction
. 1
1.2
The Least Squares Algorithm
. 2
1.3
Linear Least Squares Methods
. 3
1.3.1
Batch Least Squares Method
. 3
1.3.2
Sequential Least Squares Algorithm
. 5
1.4
Non-Linear Least Squares Algorithm
. 8
1.5
Properties of Least Squares Algorithms
. 10
1.6
Examples
. 11
1.6.1
Smooth Function Approximation
. 11
1.6.2
Star Camera Calibration
. 12
1.7
Summary
. 19
Polynomial Approximation
21
2.1
Introduction
. 21
2.2
Gram-Schmidt Procedure of Orthogonalization
. 22
2.2.1
Three-Term Recurrence Relation to Generate
Orthogonal Polynomials
. 24
2.2.2
Uniqueness of Orthogonal Polynomials
. 25
2.3
Hypergeometric Function Approach to Generate Orthogonal
Polynomials
. 30
2.3.1
Derivation of Rodrigues's Formula for Continuous
Variable Polynomials
. 34
2.3.2
Leading Coefficients for Three-Term Recurrence
Formula
. 36
2.4
Discrete Variable Orthogonal Polynomials
. 38
2.4.1
Hypergeometric Type Difference Equation
. 39
2.4.2
Derivation of Rodrigues's Formula for Discrete
Variable Orthogonal Polynomials
. 42
2.4.3
Leading Coefficients for Three-Term Recurrence
Formula for Discrete Variable Orthogonal
Polynomials
. 44
2.5
Approximation Properties of Orthogonal Polynomials
. 45
2.6
Summary
. 48
vu
Vlil
3
Artificial
Neural
Networks
for Input-Output Approximation
49
3.1
Introduction
. 49
3.1.1
Radial Basis Function Networks
. 50
3.2
Direction-Dependent Approach
. 55
3.3
Directed Connectivity Graph
. 60
3.3.1
Estimation Algorithm
. 62
3.3.2
Spectral Decomposition of the Covariance Matrix
. . 64
3.3.3
Additive Decomposition of the Covariance Matrix
. . 66
3.3.4
Cholesky Decomposition of the
Сол^агіапсе
Matrix
. . 66
3.4
Modified Minimal Resource Allocating Algorithm
(MMRAN)
. 69
3.5
Numerical Simulation Examples
. 72
3.5.1
Test Example
1:
Function Approximation
. 73
3.5.2
Test Example
2:
3-Input 1-Output Continuous
Function Approximation
. 80
3.5.3
Test Example
3:
Dynamical System Identification
. 82
3.5.4
Test Example
4:
Chaotic Time Series Prediction
. 86
3.5.5
Test Example
5:
Benchmark Against the On-Line
Structural Adaptive Hybrid Learning (OXSAHL)
Algorithm
. 90
3.6
Summary
. 93
4
Multi-Resolution Approximation Methods
95
4.1
Introduction
. 95
4.2
Wavelets
. 97
4.3
Bèzier
Spline
. 105
4.4
Moving Least Squares Method
. 110
4.5
Adaptive Multi-Resolution Algorithm
. 112
4.6
Numerical Results
. 116
4.6.1
Calibration of Vision Sensors
. 116
4.6.2
Simulation and Results
. 117
4.6.3
DCG Approximation Result
. 119
4.6.4
Local Approximation Results
. 121
4.7
Summan·
. 121
5
Global Local Orthogonal Polynomial MAPping (GLO-MAP)
in
N
Dimensions
123
5.1
Introduction
.123
5.2
Basic Ideas
.
125
5.3
Approximation in
1. 2
and
N
Dimensions Using Weighting
Functions
.128
5.4
Global-Local Orthogonal Approximation in
1-, 2-
and
.Y-Dimensional Spaces
.136
5.4.1
1-Dimensional Case
.139
■5.4.2
2-Dimensional Case
.140
їх
5.4.3
^-Dimensional Case
.142
5.5
Algorithm Implementation
.144
5.5.1
Sequential Version of the GLO-MAP Algorithm
. 146
5.6
Properties of GLO-MAP Approximation
.149
5.6.1
Approximation Error
.149
5.6.2
Bounds on Approximation Error
.150
5.6.3
Probabilistic Analysis of the GLO-MAP Algorithm
. . 152
5.7
Illustrative Engineering Applications
.155
5.7.1
Function Approximation
. 155
5.7.2
Synthetic Jet Actuator Modeling
. 160
5.7.3
Space-Based Radar (SBR) Antenna Shape
Approximation
. 166
5.7.4
Porkchop Plot Approximations for Mission to
Near-Earth Objects (NEOs)
. 170
5.8
Summary
. 174
Nonlinear System Identification
179
6.1
Introduction
.179
6.2
Problem Statement and Background
.180
6.3
Novel System Identification Algorithm
.182
6.3.1
Linear System Identification
.185
6.3.2
State Variable Estimation
.189
6.4
Nonlinear System Identification Algorithm
.190
6.4.1
Learning Algorithm for State Model Perturbation
Approach (SysID
1) .190
6.4.2
Learning Algorithm for Output Model Perturbation
Approach (SysID
2) .197
6.5
Numerical Simulation
.199
6.5.1
Dynamic System Identification of Large Space
Antenna
.199
6.6
Summary
.205
Distributed Parameter Systems
207
7.1
Introduction
. 207
7.2
MLPG-Moving Least Squares Approach
. 210
7.2.1
Poisson
Equation
. 214
7.2.2
Comments on the MLPG Algorithm
. 220
7.3
Partition of Unity Finite Element Method
. 222
7.3.1
Poisson
Equation
. 228
7.3.2
Fokker-Planck-Kolmogorov Equation
. 235
7.4
Summary
. 240
8
Control
Distribution
for Over-Actuated Systems
243
8.1
Introduction
.243
8.2
Problem Statement and Background
.245
8.3
Control Distribution Functions
.251
8.3.1
Radial Basis Functions
.254
8.3.2
Global Local Orthogonal Basis Functions
.255
8.4
Hierarchical Control Distribution Algorithm
.259
8.5
Numerical Results
.264
8.5.1
Control Allocation for a Morphing Wing
.264
8.6
Summary
.273
Appendix
275
References
285
Index
297 |
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| author | Singla, Puneet Junkins, John L. |
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| classification_rvk | SK 470 |
| ctrlnum | (OCoLC)144520994 (DE-599)GBV526139293 |
| dewey-full | 620.001/171 518.26 |
| dewey-hundreds | 600 - Technology (Applied sciences) 500 - Natural sciences and mathematics |
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| dewey-search | 620.001/171 518.26 |
| dewey-sort | 3620.001 3171 |
| dewey-tens | 620 - Engineering and allied operations 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV035139697 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:26:41Z |
| indexdate | 2024-07-09T21:23:11Z |
| institution | BVB |
| isbn | 9781584887690 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016807104 |
| oclc_num | 144520994 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XVI, 299 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | CRC Press, Taylor & Francis |
| record_format | marc |
| series | Chapman & Hall/CRC applied mathematics and nonlinear science series |
| series2 | Chapman & Hall/CRC applied mathematics and nonlinear science series |
| spelling | Singla, Puneet Verfasser aut Multi-resolution methods for modeling and control of dynamical systems Puneet Singla ; John L. Junkins Boca Raton, Fla. [u.a.] CRC Press, Taylor & Francis 2009 XVI, 299 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC applied mathematics and nonlinear science series 16 Literaturverz. S. 285 - 295 Systems engineering / Mathematical models Mathematisches Modell Systems engineering Mathematical models Dynamisches System (DE-588)4013396-5 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Approximation (DE-588)4002498-2 s DE-604 Junkins, John L. Verfasser aut Chapman & Hall/CRC applied mathematics and nonlinear science series 16 (DE-604)BV019612358 16 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016807104&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Singla, Puneet Junkins, John L. Multi-resolution methods for modeling and control of dynamical systems Chapman & Hall/CRC applied mathematics and nonlinear science series Systems engineering / Mathematical models Mathematisches Modell Systems engineering Mathematical models Dynamisches System (DE-588)4013396-5 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4002498-2 |
| title | Multi-resolution methods for modeling and control of dynamical systems |
| title_auth | Multi-resolution methods for modeling and control of dynamical systems |
| title_exact_search | Multi-resolution methods for modeling and control of dynamical systems |
| title_exact_search_txtP | Multi-resolution methods for modeling and control of dynamical systems |
| title_full | Multi-resolution methods for modeling and control of dynamical systems Puneet Singla ; John L. Junkins |
| title_fullStr | Multi-resolution methods for modeling and control of dynamical systems Puneet Singla ; John L. Junkins |
| title_full_unstemmed | Multi-resolution methods for modeling and control of dynamical systems Puneet Singla ; John L. Junkins |
| title_short | Multi-resolution methods for modeling and control of dynamical systems |
| title_sort | multi resolution methods for modeling and control of dynamical systems |
| topic | Systems engineering / Mathematical models Mathematisches Modell Systems engineering Mathematical models Dynamisches System (DE-588)4013396-5 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | Systems engineering / Mathematical models Mathematisches Modell Systems engineering Mathematical models Dynamisches System Approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016807104&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019612358 |
| work_keys_str_mv | AT singlapuneet multiresolutionmethodsformodelingandcontrolofdynamicalsystems AT junkinsjohnl multiresolutionmethodsformodelingandcontrolofdynamicalsystems |