Discrete linear control systems:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English Russian |
Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1991
|
Schriftenreihe: | Mathematics and its applications
Soviet series ; 67 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | Aus dem Russ. übers. |
Beschreibung: | XIII, 302 S. |
ISBN: | 0792312481 |
Internformat
MARC
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100 | 1 | |a Fomin, Vladimir N. |d 1937-2000 |e Verfasser |0 (DE-588)131358073 |4 aut | |
240 | 1 | 0 | |a Metody upravlenija linejnymi diskretnymi ob'ektami |
245 | 1 | 0 | |a Discrete linear control systems |c by V. N. Fomin |
264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1991 | |
300 | |a XIII, 302 S. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
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490 | 1 | |a Mathematics and its applications : Soviet series |v 67 | |
500 | |a Aus dem Russ. übers. | ||
650 | 4 | |a Commande, Théorie de la | |
650 | 7 | |a commande adaptative |2 inriac | |
650 | 7 | |a estimation récursive |2 inriac | |
650 | 7 | |a filtre Kalman-Bucy |2 inriac | |
650 | 7 | |a formule Bayes |2 inriac | |
650 | 7 | |a identification système |2 inriac | |
650 | 7 | |a minimax |2 inriac | |
650 | 7 | |a optimisation linéaire |2 inriac | |
650 | 7 | |a programmation dynamique |2 inriac | |
650 | 7 | |a système linéaire discret |2 inriac | |
650 | 7 | |a théorie commande |2 inriac | |
650 | 4 | |a Control theory | |
650 | 0 | 7 | |a Regelungstheorie |0 (DE-588)4122327-5 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Lineares System |0 (DE-588)4125617-7 |2 gnd |9 rswk-swf |
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689 | 0 | 1 | |a Lineares System |0 (DE-588)4125617-7 |D s |
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Datensatz im Suchindex
_version_ | 1804118919840006144 |
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adam_text | CONTENTS
Series Editor s Preface v
Preface (to the Russian Edition) vii
Chapter 1 Basic concepts and statement of problems in control theory 1
1.1 Initial premises 1
1.2 Basic concepts of control theory 2
1.2.1 The control object 2
1.2.2 Control algorithm 3
1.2.3 Control objective 5
1.3 Modelling of control objects and their general characteristics 7
1.3.1 State equations of discrete processes 7
1.3.2 Observability and controllability 8
1.3.3 Linear proces 8
1.4 Precising the statement of the control problem 11
1.4.1 Classification of control objectives 11
1.4.2 Optimisation of control 11
1.4.3 Observations on selection of control strategies 12
Chapter 2 Finite time period control 13
2.1 Dynamic programming 13
2.1.1 Statement of the optimization problem 13
2.1.2 Description of the Dynamic programming methods 13
2.1.3 Bellman s equation 15
2.1.4 Example: Linear quadratic deterministic system 16
2.1.5 Generalisation of Bellman s equation for infinite time control
problems 17
2.2 Stochastic control systems 18
2.2.1 Statement of the problem 18
2.2.2 Dependence of the optimal solution on the choice of the admissible
control strategies 19
2.3 Stochastic dynamic programming 21
2.3.1 Description of the method 21
2.3.2 Bellman s equation for stochastic control systems 22
2.3.3 Example: Linear quadratic problem with randomly varying coeffi¬
cients and observable states of the control object 23
2.3.4 Example: Linear stationary object with control delay 24
2.4 Bayesian control strategy 26
2.4.1 Bayesian approach to the optimization problem 27
2.4.2 A posteriori distribution and Bayesian formula 28
2.4.3 Regularity in Bayesian control strategy 30
2.4.4 Recursive formulae for computations of a posteriori distributions 31
2.5 Linear quadratic Gaussian Problem 33
2.5.1 Statement of the problem 3 3
2.5.2 Conditional Gaussism of the states and sufficient statistics 34
X
2.5.3 Bayesian control strategy 35
2.A Appendix 36
2. A. 1 General forms of probability theory 36
2.A.2 Convergence of random variables 37
2.P Proofs of lemmas and theorems 38
2.P.1 Proof of the theorem 2.1.1 38
2.P.2 Proof of the theorem 2.1.2 39
2.P.3 Proof of the theorem 2.3.1 39
2.P.4 Proof of the lemma 2.3.1 40
2.P.5 Proof of the theorem 2.3.2. 40
2.P.6 Proof of the lemma 2.4.1 40
2.P.7 Proof of the theorem 2.4.1 41
2.P.8 Proof of the theorem 2.4.2. 42
Chapter 3 Infinite time period control 43
3.1 Stabilitzation of dynamic systems using Liapunov s method 43
3.1.1 Description of Liapunov s method 44
3.1.2 Stabilization of linear systems with observable states 45
3.1.3 Stabilization of linear systems with unobservable states 49
3.2 Discrete form for analytical design of regulators 51
3.2.1 Statement of the problem 51
3.2.2 Reduction of the optimization problem to the solvability of the matrix
Riccati equation 52
3.2.3 Lur e equation and a few of its properties 53
3.2.4 Analytical design of regulators in the presence of additive noise 58
3.3 Transfer function method in linear optimization problem 61
3.3.1 Statement of the linear optimization problem 61
3.3.2 Transfer functions of control systems and their properties 62
3.3.3 Geometrical interpretation of the linear optimization problem 64
3.3.4 Weiner Kolmogorov method for conditional minimization of a
quadratic functional 64
3.3.5 Parametrization of the set of transfer functions 65
3.3.6 Design of the optimal regulator for the object expressed in the stan¬
dard form 66
3.3.7 Correspondence between transfer function method and method of
Lur e solving equation 69
3.3.8 Design of the optimal regulator for control object equations expressed
through input output variables 69
3.4 Limiting optimal control of stochastic processes 74
3.4.1 Sufficient conditions for optimality of admissible control strategies 75
3.4.2 Statement of the limiting linear quadratic optimal control problem 76
3.4.3 Solvability of the optimization problem 77
3.4.4 Design of optimal linear regulators through transfer function method 83
3.4.5 Formulation of the limited optimal control problems using Riccati
equation 94
3.5 Minimax control 96
xi
3.5.1 Statement of the minimax control problem 96
3.5.2 Control system transfer function and its properties 97
3.5.3 Geometrical interpretation of the minimax control problem 98
3.5.4 Properties of the sets in geometrical interpretation of the optimization
problem 100
3.5.5 Statement of the basic result 103
3.5.6 The Properties of the optimal regulator 104
3.5.7 A few generalisations 105
3.A Appendix 108
3.A.I Frequency theorem 108
3.P Proofs of the lemmas and theorems 109
3.P. 1 Proof of the theorem 3.1.1 109
3.P.2 Proof of the theorem 3.1.2 109
3.P.3 Proof of the theorem 3.1.3 110
3.P.4 Proofofthe theorem 3.1.4 110
3.P.5 Proof of the theorem 3.2.1 111
3.P.6 Proof of the theorem 3.2.2 112
3.P.7 Proofofthe theorem 3.3.1 115
3.P.8 Proof of the lemma 3.3.1 118
3.P.9 Proof of the theorem 3.3.2 119
3.P.10 Proofofthe lemma 3.3.2 120
3.P.11 Proof of the theorem 3.3.3 122
3.P.12 Proofofthe lemma 3.3.3 122
3.P.13 Proofofthe lemma 3.3.4 123
3.P.14 Proof of the theorem 3.4.1 124
3.P.15 Proof of the theorem 3.4.2 124
3.P.16 Proof of the theorem 3.4.3 125
3.P.17 Proofofthe theorem 3.4.4 127
3.P.18 Proofofthe theorem 3.4.5 127
3.P.19 Proofofthe theorem 3.4.1 130
3.P.20 Proof of the lemma 3.4.2 130
3.P.21 Proofofthe theorem 3.4.6 132
3.P.22 Proof of the theorem 3.4.7 133
3.P.23 Proofofthe lemma 3.4.3 135
3.P.24 Proofofthe theorem 3.5.1 136
3.P.25 Proofofthe theorem 3.5.2 137
Chapter 4 Adaptive linear control systems with bounded noise 138
4.1 Fundamentals of adaptive control 140
4.1.1 Adaptive control strategy 140
4.1.2 Identification method in adaptive control 141
4.2 Existence of adaptive control strategy in a minimax control problem 143
4.2.1 Statement of the problem 144
4.2.2 Synthesis of an adaptive control strategy 146
4.2.3 Examples 148
4.3 Self tuning systems 149
xii
4.3.1 Self tuning with no disturbance 150
4.3.2 Self tuning in the presence of disturbance 152
4.3.3 Adaptive control with bounded disturbance in the control object 155
4.3.4 Method of recursive objective inequalities in an adaptive tracking
problem 158
4.P Proofs of the lemmas and theorems 162
4.P. 1 Proof of the lemma 4.2.1 162
4.P.2 Proof of the theorem 4.2.1. 163
4.P.3 Proof of the theorem 4.3.1 164
4.P.4 Proof of the theorem 4.3.2 165
4.P.5 Proof of the theorem 4.3.3 167
4.P.6 Proof of the theorem 4.3.4 168
Chapter 5 The problem of dynamic system identification 169
5.1 Optimal recursive estimation 169
5.1.1 Formulation of the estimation problems 170
5.1.2 Duality of the estimation and optimal control problems 171
5.1.3 Solution of the matrix linear quadratic cost optimization problem 172
5.1.4 The Kalman Bucy filter 173
5.1.5 Optimal properties of the Kalman Bucy filter 174
5.2 The Kalman Bucy filter for tracking the parameter drift in dynamic systems 177
5.2.1 Optimal tracking of the parameter drift in presence of Gaussian
disturbances 178
5.2.2 Asymptotic properties of the Kalman Bucy filter 180
5.3 Recursive estimation 184
5.3.1 Forecasting methods of identification 184
5.3.2 Selection of forecasting models 185
5.3.3 Recursive schemes for estimation 190
5.4 Identification of a linear control object in the presence of correlated noise 192
5.4.1 Uniqueness of the minimum of the forecasting performance criterion 193
5.4.2 Modification of the estimation algorithm 194
5.4.3 Consistency of the estimates of the identification algorithm 195
5.4.4 Identification of linear systems with known spectral density of noise 196
5.5 Identification of control objects using test signals 198
5.5.1 Statement of the identification problem 198
5.5.2 Introduction of the estimation parameter 199
5.5.3 Estimation algorithm 199
5.5.4 Consistency of the estimates 200
5.P Proofs of lemmas and theorems 201
5.P. 1 Proof of the theorem 5.1.1 201
5.P.2 Proof of the lemma 5.1.1 202
5.P.3 Proof of the lemma 5.1.2 202
5.P.4 Proof of the lemma 5.1.3 203
5.P.5 Proof of the theorem 5.2.1 204
5.P.6 Proof of the theorem 5.2.2 207
5.P.7 Proof of the theorem 5.2.3 208
xiii
5.P.8 Proof of the theorem 5.2.4 209
5.P.9 Proof of the lemma 5.4.1 212
5.P.10 Proof of the lemma 5.4.2 213
5.P. 11 Proof of the theorem 5.4.1 215
5.P.12 Proof of the theorem 5.4.2 216
5.P.13 Proof of the lemma 5.5.1 217
5.P.14 Proof of the theorem 5.5.1 218
Chapter 6 Adaptive control of stochastic systems 221
6.1 Dual control 221
6.1.1 Bayesian approach to adaptive control problems 223
6.1.2 Adaptive version of the Gaussian linear quadratic control problems,
with observable vector states 225
6.1.3 Bayesian control strategy 231
6.1.4 Recursive relations for a posteriori distributions 236
6.2 Initial synthesis of adaptive control strategy in presence of the correlated noise 243
6.2.1 Adaptive optimal control for a performance criterion dependent on
events 243
6.2.2 Direct method of adaptive control formulation 250
6.2.3 Adaptive optimization of the unconditional performance criterion 255
6.3 Design of the adaptive minimax control 259
6.3.1 Statement of the problem 260
6.3.2 Formulation of the adaptive control strategy 261
6.P Proofs of the lemmas and the theorems 261
6.P. 1 Proof of the theorem 6.1.1 261
6.P.2 Proof of the theorem 6.1.2 262
6.P.3 Proof of the lemma 6.2.1 262
6.P.4 Proof of the lemma 6.2.2 266
6.P.5 Proof of the lemma 6.2.3 266
6.P.6 Proof of the lemma 6.2.4 267
6.P.7 Proof of the lemma 6.2.5 268
6.P.8 Proof of the theorem 6.2.1 269
6.P.9 Proof of the theorem 6.2.2 277
6.P.10 Proof of the theorem 6.2.3 278
6.P.11 Proof of the lemma 6.2.6 279
6.P.12 Proof of the theorem 6.2.4 280
6.P.13 Proof of the lemma 6.2.7 281
6.P.14 Proof of the theorem 6.2.5 282
6.P.15 Proof of the theorem 6.3.1 283
COMMENTS 285
REFERENCES 289
OPERATORS AND NOTATIONAL CONVENTIONS 298
SUBJECT INDEX 300
|
any_adam_object | 1 |
author | Fomin, Vladimir N. 1937-2000 |
author_GND | (DE-588)131358073 |
author_facet | Fomin, Vladimir N. 1937-2000 |
author_role | aut |
author_sort | Fomin, Vladimir N. 1937-2000 |
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dewey-hundreds | 600 - Technology (Applied sciences) |
dewey-ones | 629 - Other branches of engineering |
dewey-raw | 629.8/312 |
dewey-search | 629.8/312 |
dewey-sort | 3629.8 3312 |
dewey-tens | 620 - Engineering and allied operations |
discipline | Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
format | Book |
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id | DE-604.BV004807928 |
illustrated | Not Illustrated |
indexdate | 2024-07-09T16:17:57Z |
institution | BVB |
isbn | 0792312481 |
language | English Russian |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002957734 |
oclc_num | 23584145 |
open_access_boolean | |
owner | DE-12 DE-29T DE-91 DE-BY-TUM |
owner_facet | DE-12 DE-29T DE-91 DE-BY-TUM |
physical | XIII, 302 S. |
publishDate | 1991 |
publishDateSearch | 1991 |
publishDateSort | 1991 |
publisher | Kluwer |
record_format | marc |
series | Mathematics and its applications |
series2 | Mathematics and its applications : Soviet series |
spelling | Fomin, Vladimir N. 1937-2000 Verfasser (DE-588)131358073 aut Metody upravlenija linejnymi diskretnymi ob'ektami Discrete linear control systems by V. N. Fomin Dordrecht [u.a.] Kluwer 1991 XIII, 302 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications : Soviet series 67 Aus dem Russ. übers. Commande, Théorie de la commande adaptative inriac estimation récursive inriac filtre Kalman-Bucy inriac formule Bayes inriac identification système inriac minimax inriac optimisation linéaire inriac programmation dynamique inriac système linéaire discret inriac théorie commande inriac Control theory Regelungstheorie (DE-588)4122327-5 gnd rswk-swf Lineares System (DE-588)4125617-7 gnd rswk-swf Regelungstheorie (DE-588)4122327-5 s Lineares System (DE-588)4125617-7 s DE-604 Mathematics and its applications Soviet series ; 67 (DE-604)BV004708148 67 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002957734&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Fomin, Vladimir N. 1937-2000 Discrete linear control systems Mathematics and its applications Commande, Théorie de la commande adaptative inriac estimation récursive inriac filtre Kalman-Bucy inriac formule Bayes inriac identification système inriac minimax inriac optimisation linéaire inriac programmation dynamique inriac système linéaire discret inriac théorie commande inriac Control theory Regelungstheorie (DE-588)4122327-5 gnd Lineares System (DE-588)4125617-7 gnd |
subject_GND | (DE-588)4122327-5 (DE-588)4125617-7 |
title | Discrete linear control systems |
title_alt | Metody upravlenija linejnymi diskretnymi ob'ektami |
title_auth | Discrete linear control systems |
title_exact_search | Discrete linear control systems |
title_full | Discrete linear control systems by V. N. Fomin |
title_fullStr | Discrete linear control systems by V. N. Fomin |
title_full_unstemmed | Discrete linear control systems by V. N. Fomin |
title_short | Discrete linear control systems |
title_sort | discrete linear control systems |
topic | Commande, Théorie de la commande adaptative inriac estimation récursive inriac filtre Kalman-Bucy inriac formule Bayes inriac identification système inriac minimax inriac optimisation linéaire inriac programmation dynamique inriac système linéaire discret inriac théorie commande inriac Control theory Regelungstheorie (DE-588)4122327-5 gnd Lineares System (DE-588)4125617-7 gnd |
topic_facet | Commande, Théorie de la commande adaptative estimation récursive filtre Kalman-Bucy formule Bayes identification système minimax optimisation linéaire programmation dynamique système linéaire discret théorie commande Control theory Regelungstheorie Lineares System |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002957734&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV004708148 |
work_keys_str_mv | AT fominvladimirn metodyupravlenijalinejnymidiskretnymiobektami AT fominvladimirn discretelinearcontrolsystems |