Operator approach to linear control systems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1996
|
| Schriftenreihe: | Mathematics and its applications
345 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 396 S. |
| ISBN: | 0792337654 |
Internformat
MARC
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| 001 | BV011124238 | ||
| 003 | DE-604 | ||
| 005 | 20060621 | ||
| 007 | t | ||
| 008 | 961219s1996 |||| 00||| eng d | ||
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| 035 | |a (DE-599)BVBBV011124238 | ||
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| 041 | 0 | |a eng | |
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| 082 | 0 | |a 629.8/32 |2 20 | |
| 100 | 1 | |a Čeremenski, A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Operator approach to linear control systems |c by A. Cheremensky and V. Fomin |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c 1996 | |
| 300 | |a XVI, 396 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 345 | |
| 650 | 7 | |a Commande linéaire |2 ram | |
| 650 | 4 | |a Linear control systems | |
| 650 | 0 | 7 | |a Lineares Regelungssystem |0 (DE-588)4167730-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Operatortheorie |0 (DE-588)4075665-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineares Regelungssystem |0 (DE-588)4167730-4 |D s |
| 689 | 0 | 1 | |a Operatortheorie |0 (DE-588)4075665-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Fomin, Vladimir N. |d 1937-2000 |e Verfasser |0 (DE-588)131358073 |4 aut | |
| 830 | 0 | |a Mathematics and its applications |v 345 |w (DE-604)BV008163334 |9 345 | |
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| 940 | 1 | |n oe | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007453717 | ||
Datensatz im Suchindex
| _version_ | 1804125615619571712 |
|---|---|
| adam_text | Contents
Preface xi
1 Introduction 1
1.1 Basic notions of systems theory 1
1.1.1 Plants as input output mapping 2
1.1.2 Free and external variables 3
1.1.3 Controllers 3
1.1.4 Transfer system operators 5
1.1.5 Optimal control 5
1.1.6 Stochastic control 7
1.1.7 Separation principle 8
1.1.8 Uncertainty in control problems 8
2 Introduction to systems theory 11
2.1 Linear system and its transfer operators 11
2.2 Example: one dimensional time invariant linear system 13
2.3 System operator enlargements and parameterizations of the set
of system solutions 15
2.4 Remark 18
2.5 Example: one dimensional control plant of first order 20
2.6 Some optimization problems 23
2.6.1 Projection lemmas 23
2.6.2 Robustness 24
3 Resolution spaces 27
3.1 Hilbert space 27
3.1.1 Extended and equipped spaces 27
3.1.2 Classes of transforms in Hilbert space 30
3.1.3 Stochastic elements with their values in an extended space 33
v
vi Contents
3.1.4 Stochastic processes as generalized elements of Hilbert
space 34
3.2 Hilbert resolution space 36
3.2.1 Resolution of identity 36
3.2.2 Structure of Hilbert resolution space 37
3.2.3 Examples of discrete and absolute continuous resolution
Hilbert space 39
3.2.4 Functional representation of an abstract Hilbert resolu¬
tion space 41
3.3 Space extension endowed with time structure 43
3.3.1 Equipped Hilbert resolution space 43
3.3.2 Equipped separable resolution space 44
3.3.3 Resolution structure of extended space 45
3.3.4 Integral representation of elements in extended Hilbert
resolution space 48
3.3.5 Localized elements of extended resolution space 49
3.3.6 Example of localized elements in L2 50
3.3.7 Example of localized elements in discrete resolution space 51
3.3.8 Frequency representation of elements of an absolutely
continuous Hilbert resolution space 52
3.3.9 Frequency representation of discrete Hilbert resolu¬
tion space 54
3.4 Operators in resolution spaces 56
3.4.1 Operators in Hilbert resolution space 56
3.4.2 Linear integral operators in L2(R) 57
3.4.3 Additive operators 58
3.4.4 Causal operators in extended resolution space 59
3.4.5 Block representation of linear operators in extended causal
space 61
3.4.6 Block representation of integral operator in L2 63
3.4.7 Closing of operators in extended resolution space .... 64
3.4.8 Adjoint operators in extended resolution space 65
3.4.9 Linear time invariant differential system operators ... 66
3.4.10 Linear operator factorization in an extended resolution
space 70
3.4.11 Linear operator separation in an extended resolution space 75
3.5 Linear time invariant differential system operators 75
3.5.1 Frequency description of time invariant closed loop sys¬
tems 75
3.5.2 Transfer matrix function of linear time invariant system 77
3.5.3 Robustness of time invariant differential linear systems . 79
3.5.4 Generalized Fourier transform 80
3.6 Stationary operators 84
3.6.1 Stationary operators in continuous time 84
Contents vii
3.6.2 Symbol of stationary operator 85
3.6.3 Stationary operator factorization 86
3.6.4 Generalized Fourier transform in L2(n,R+) 87
3.6.5 Stationary operators in discrete resolution space .... 88
3.6.6 Time invariant (stationary) operators acting from one
resolution space to another 91
4 Linear control plants in a resolution space 93
4.1 Some control problems 93
4.1.1 A linear control plant 93
4.1.2 Admissible control strategies 97
4.1.3 Control aims 100
4.2 Feedback problem 102
4.3 Feedback in linear structured systems 106
4.3.1 Gauss method application 107
4.3.2 Separation principle 110
4.4 Design of time invariant systems with fixed space variables . . 114
4.4.1 Examples of time invariant systems with fixed space
variables 114
4.5 Constructing transfer operators for some time invariant plants . 118
4.5.1 Corona problem 118
4.5.2 Polynomial technique 123
4.5.3 Larin compensator 125
4.5.4 Lagrange Sylvester interpolation 126
4.5.5 Neutral systems 128
4.6 Robustness of stationary differential closed loop systems .... 130
4.6.1 Degenerate systems 131
4.6.2 Time invariant difference differential system 133
4.6.3 Estimation of robustness domain 134
5 Linear quadratic optimization in preplanned control class 137
5.1 Preplanned optimal controls 137
5.1.1 Setting of problem 138
5.1.2 Lagrange multiplier method 145
5.2 Linear quadratic game problem of optimal preplanned control . 150
5.3 Feedback form of preplanned stochastic optimal control .... 153
5.3.1 Refining the optimal control problem setting 153
5.3.2 Solving the problem of preplanned optimal control . . . 156
5.3.3 Problem of preplanned optimal control with time structure 157
5.3.4 Operator Bellman equation 160
5.3.5 Riccati equation 161
5.3.6 Example: Riccati equation in Markovian case 164
5.3.7 Optimal control and Riccati equation 167
5.3.8 Stationary feedback and Lur e equation 167
viii Contents
5.4 Special representation of control criteria 169
5.4.1 General assertion 169
5.4.2 Outlines of the general assertion proof and some re¬
marks 170
5.4.3 Optimal feedback for known external disturbances . . . 172
5.4.4 Factorization of the weight operator 174
5.5 Design of the preplanned optimal control 175
5.5.1 Statement of the problem of preplanned control .... 175
5.5.2 Necessary condition of the optimal control problem solv¬
ability 176
5.5.3 Solving of the problem of preplanned optimal control . 177
5.5.4 Limit optimal preplanned control 179
6 Linear quadratic optimization in feedback control class 181
6.1 Existence of optimal feedback 181
6.1.1 Objective setting 181
6.1.2 Solvability of LQP 182
6.1.3 Modification of the optimal LQP 184
6.1.4 Minimax optimal problem . 185
6.2 Abstract variant of the Wiener problem 185
6.2.1 Statement of the operator Wiener problem 186
6.2.2 Scalar variant of Wiener problem 188
6.2.3 Generalized Wiener problem solving on the set of local¬
ized elements 190
6.2.4 Generalized Wiener problem solving on the set of finite
localized elements 191
6.2.5 Solving the operator Wiener problem in discrete reso¬
lution space 195
6.2.6 Wiener problem in stationary case 197
6.3 Wiener method in LQP 199
6.3.1 Objective setting of abstract control problem 199
6.3.2 Remarks on setting abstract control problem 201
6.3.3 Transformation of the abstract control problem into the
Wiener problem 205
6.3.4 Linear quadratic problem and Pareto optimal control . 207
6.3.5 Wiener problem solvability 208
6.4 Optimal design 211
6.4.1 Linear quadratic problem in Hilbert space 211
6.4.2 Solving the control problem in the set of admissible
transform operators 214
6.4.3 Example: finite dimensional time invariant control system218
6.5 Systems with incomplete and noisy measurements 223
6.5.1 Example: Linear time invariant singular input singular
output plant 225
Contents ix
6.6 Special representation in case of incomplete and noisy measure¬
ments 228
6.6.1 Optimal control in discrete resolution space 228
6.6.2 Linear optimal filtering of stochastic time series .... 230
6.6.3 Separation principle 233
6.6.4 Luenberger observer 235
6.6.5 Kalman Bucy filter 239
6.7 Design of the optimal stabilizing feedback for finite dimensional
time invariant plant 242
6.7.1 Setting of an optimal control problem 242
6.7.2 Operator reformulation of the optimal control problem . 247
6.7.3 Frequency reformulation of the optimal control problem 250
6.7.4 Design of the optimal control system transfer function . 251
6.7.5 Remarks on the optimal feedback design 253
6.7.6 Optimal feedback design in discrete case 257
6.7.7 Example: optimal stabilizing feedback for stable and
miniphase plant 265
6.7.8 Optimal control in case of no noises 266
7 Finite dimensional LQP 271
7.1 Stochastic linear quadratic problem on a finite time interval . 272
7.1.1 Setting of the stochastic linear quadratic problem . . . 272
7.1.2 Example: optimal control problem in case of known
states and noises 273
7.1.3 Synthesis of feedback in case of incomplete observation
data 274
7.1.4 Example: dependence of optimal control from the choice
of control strategies set 276
7.2 General method of optimal control synthesis 277
7.2.1 Separation theorem 278
7.2.2 Synthesis of the optimal control strategy 283
7.2.3 Example: synthesis of the optimal control for random
initial state 284
7.2.4 Kalman Bucy filter in optimal control 286
7.2.5 Optimal tracking problem 288
7.2.6 Nonlinear optimal feedbacks 290
7.2.7 Example: scalar plant with finite valued disturbance . 292
7.3 Time invariant SLQP on the infinite time interval 294
7.3.1 Stochastic optimal control problem setting 294
7.3.2 Reformulation of control problem 297
7.3.3 Wiener problem connected with optimal control .... 298
7.3.4 Solvability of SLQP 300
7.3.5 Wiener method of solving LQP 301
7.3.6 Design of the optimal feedback 302
x Contents
7.4 Extended control problem 302
7.4.1 Optimization problem in the set of preplanned control 303
7.4.2 Solvability of the extended problem 306
7.4.3 Solvability of the extended problem 307
7.4.4 Design of the optimal control in SLQP for linear time
invariant plant 309
7.4.5 Design of optimal feedback for known plant states
and noise realizations 311
7.4.6 Design of optimal feedback for unknown plant states
and noise realizations 313
7.4.7 Recursive algorithm for the Wiener estimations 314
8 Some computing methods in stationary finite dimensional
SLQPs 317
8.1 Algebraic methods of spectral factorization of rational matrix
functions on the unit circle 317
8.1.1 Youla factorization method 318
8.1.2 Lur e equation method 319
8.1.3 Spectral factorization of matrix polynomial positive on
the unit circle 320
8.1.4 Letov approach 322
8.1.5 Orthogonal projection method 324
8.2 Iterative methods of rational factorization and separation . . . 325
8.2.1 Riccati equation method 325
8.2.2 Orthogonal projection method 325
8.2.3 Rational separation 330
8.2.4 Stability enhancing scaling procedure 331
8.2.5 Newton Raphson method 331
8.2.6 Fast matrix inversion 333
8.2.7 Spectral factorization and frequency theorem 336
8.2.8 Method of extended LQP 340
8.2.9 Reduction of positive polynomial factorization problem
to solving linear algebraic systems 343
8.2.10 Illustration of spectral factorization methods 347
8.2.11 Solving Lur e equation by the orthoprojection method . 352
8.3 Appendix 354
Comments 359
References 371
Notations and conventions 387
Index 391
|
| any_adam_object | 1 |
| author | Čeremenski, A. Fomin, Vladimir N. 1937-2000 |
| author_GND | (DE-588)131358073 |
| author_facet | Čeremenski, A. Fomin, Vladimir N. 1937-2000 |
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| discipline | Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
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| id | DE-604.BV011124238 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:04:23Z |
| institution | BVB |
| isbn | 0792337654 |
| language | English |
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| physical | XVI, 396 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Čeremenski, A. Verfasser aut Operator approach to linear control systems by A. Cheremensky and V. Fomin Dordrecht [u.a.] Kluwer Acad. Publ. 1996 XVI, 396 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 345 Commande linéaire ram Linear control systems Lineares Regelungssystem (DE-588)4167730-4 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Lineares Regelungssystem (DE-588)4167730-4 s Operatortheorie (DE-588)4075665-8 s DE-604 Fomin, Vladimir N. 1937-2000 Verfasser (DE-588)131358073 aut Mathematics and its applications 345 (DE-604)BV008163334 345 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007453717&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Čeremenski, A. Fomin, Vladimir N. 1937-2000 Operator approach to linear control systems Mathematics and its applications Commande linéaire ram Linear control systems Lineares Regelungssystem (DE-588)4167730-4 gnd Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4167730-4 (DE-588)4075665-8 |
| title | Operator approach to linear control systems |
| title_auth | Operator approach to linear control systems |
| title_exact_search | Operator approach to linear control systems |
| title_full | Operator approach to linear control systems by A. Cheremensky and V. Fomin |
| title_fullStr | Operator approach to linear control systems by A. Cheremensky and V. Fomin |
| title_full_unstemmed | Operator approach to linear control systems by A. Cheremensky and V. Fomin |
| title_short | Operator approach to linear control systems |
| title_sort | operator approach to linear control systems |
| topic | Commande linéaire ram Linear control systems Lineares Regelungssystem (DE-588)4167730-4 gnd Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Commande linéaire Linear control systems Lineares Regelungssystem Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007453717&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT ceremenskia operatorapproachtolinearcontrolsystems AT fominvladimirn operatorapproachtolinearcontrolsystems |