Partially observable linear systems under dependent noises
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Birkhäuser
2003
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| Schriftenreihe: | Systems & Control
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| 100 | 1 | |a Bashirov, Agamirza E. |e Verfasser |0 (DE-588)124392865 |4 aut | |
| 245 | 1 | 0 | |a Partially observable linear systems under dependent noises |c Agamirza E. Bashirov |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2003 | |
| 300 | |a XXVI, 334 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Systems & Control | |
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| 650 | 0 | 7 | |a Stochastische optimale Kontrolle |0 (DE-588)4207850-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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|---|---|
| adam_text | AGAMIRZA E. BASHIROV PARTIALLY OBSERVABLE LINEAR SYSTEMS UNDER DEPENDENT
NOISES BIRKHAUSER VERLAG BASEL * BOSTON * BERLIN CONTENTS PREFACE XV 1
BASIC ELEMENTS OF FUNCTIONAL ANALYSIS 1 1.1 SETS AND FUNCTIONS 1 1.1.1
SETS AND QUOTIENT SETS 1 1.1.2 SYSTEMS OF NUMBERS AND CARDINALITY 2
1.1.3 SYSTEMS OF SETS 3 1.1.4 FUNCTIONS AND SEQUENCES 4 1.2 ABSTRACT
SPACES 5 1.2.1 LINEAR SPACES 5 1.2.2 METRIC SPACES 6 1.2.3 BANACH SPACES
8 1.2.4 HILBERT AND EUCLIDEAN SPACES 9 1.2.5 MEASURABLE AND BOREL SPACES
10 1.2.6 MEASURE AND PROBABILITY SPACES 11 1.2.7 PRODUCT OF SPACES 13
1.3 LINEAR OPERATORS 15 1.3.1 BOUNDED OPERATORS 15 1.3.2 INVERSE
OPERATORS 17 1.3.3 CLOSED OPERATORS 19 1.3.4 ADJOINT OPERATORS 19 1.3.5
PROJECTION OPERATORS 20 1.3.6 SELF-ADJOINT, NONNEGATIVE AND COERCIVE
OPERATORS 21 1.3.7 COMPACT, HILBERT-SCHMIDT AND NUCLEAR OPERATORS 22 1.4
WEAK CONVERGENCE 26 1.4.1 STRONG AND WEAK FORMS OF CONVERGENCE 26 1.4.2
WEAK CONVERGENCE AND CONVEXITY 27 1.4.3 CONVERGENCE OF OPERATORS 28 2
BASIC CONCEPTS OF ANALYSIS IN ABSTRACT SPACES 31 2.1 CONTINUITY 31 2.1.1
CONTINUITY OF VECTOR-VALUED FUNCTIONS 31 2.1.2 WEAK LOWER SEMICONTINUITY
32 CONTENTS 2.1.3 CONTINUITY OF OPERATOR-VALUED FUNCTIONS 33 2.2
DIFFERENTIABILITY 34 2.2.1 DIFFERENTIABILITY OF NONLINEAR OPERATORS 34
2.2.2 DIFFERENTIABILITY OF OPERATOR-VALUED FUNCTIONS 36 2.3
MEASURABILITY 37 2.3.1 MEASURABILITY OF VECTOR-VALUED FUNCTIONS 37 2.3.2
MEASURABILITY OF OPERATOR-VALUED FUNCTIONS 39 2.3.3 MEASURABILITY OF CJ-
AND 2-VALUED FUNCTIONS 39 2.4 INTEGRABILITY 41 2.4.1 BOCHNER INTEGRAL
42 2.4.2 FUBINI S PROPERTY 45 2.4.3 CHANGE OF VARIABLE 47 2.4.4 STRONG
BOCHNER INTEGRAL 49 2.4.5 BOCHNER INTEGRAL OF C - AND ^2-VALUED
FUNCTIONS 52 2.5 INTEGRAL AND DIFFERENTIAL OPERATORS 52 2.5.1 INTEGRAL
OPERATORS 52 2.5.2 INTEGRAL HUBERT-SCHMIDT OPERATORS 53 2.5.3
DIFFERENTIAL OPERATORS 55 2.5.4 GRONWALL S INEQUALITY AND CONTRACTION
MAPPINGS 58 EVOLUTION OPERATORS 59 3.1 MAIN CLASSES OF EVOLUTION
OPERATORS 59 3.1.1 STRONGLY CONTINUOUS SEMIGROUPS 59 3.1.2 EXAMPLES 60
3.1.3 MILD EVOLUTION OPERATORS 64 3.2 TRANSFORMATIONS OF EVOLUTION
OPERATORS 66 3.2.1 BOUNDED PERTURBATIONS 66 3.2.2 SOME OTHER
TRANSFORMATIONS 70 3.3 OPERATOR RICCATI EQUATIONS 71 3.3.1 EXISTENCE AND
UNIQUENESS OF SOLUTION 71 3.3.2 DUAL RICCATI EQUATION 75 3.3.3 RICCATI
EQUATIONS IN DIFFERENTIAL FORM 77 3.4 UNBOUNDED PERTURBATION 80 3.4.1
PRELIMINARIES 80 3.4.2 A*-PERTURBATION 82 3.4.3 A-PERTURBATION 85 3.4.4
EXAMPLES 87 PARTIALLY OBSERVABLE LINEAR SYSTEMS 93 4.1 RANDOM VARIABLES
AND PROCESSES 93 4.1.1 RANDOM VARIABLES 93 4.1.2 CONDITIONAL EXPECTATION
AND INDEPENDENCE 95 4.1.3 GAUSSIAN SYSTEMS 97 4.1.4 RANDOM PROCESSES 98
CONTENTS XI 4.2 STOCHASTIC MODELLING OF REAL PROCESSES 101 4.2.1
BROWNIAN MOTION 101 4.2.2 WIENER PROCESS MODEL OF BROWNIAN MOTION 104
4.2.3 DIFFUSION PROCESSES 105 4.3 STOCHASTIC INTEGRATION IN HILBERT
SPACES 106 4.3.1 STOCHASTIC INTEGRAL 106 4.3.2 MARTINGALE PROPERTY 108
4.3.3 FUBINI S PROPERTY 109 4.3.4 STOCHASTIC INTEGRATION WITH RESPECT TO
WIENER PROCESSES . . ILL 4.4 PARTIALLY OBSERVABLE LINEAR SYSTEMS 113
4.4.1 SOLUTION CONCEPTS 113 4.4.2 LINEAR STOCHASTIC EVOLUTION SYSTEMS
115 4.4.3 PARTIALLY OBSERVABLE LINEAR SYSTEMS 117 4.5 BASIC ESTIMATION
IN HILBERT SPACES 117 4.5.1 ESTIMATION OF RANDOM VARIABLES 117 4.5.2
ESTIMATION OF RANDOM PROCESSES 120 4.6 IMPROVING THE BROWNIAN MOTION
MODEL 122 4.6.1 WHITE, COLORED AND WIDE BAND NOISE PROCESSES 122 4.6.2
INTEGRAL REPRESENTATION OF WIDE BAND NOISES 125 5 SEPARATION PRINCIPLE
129 5.1 SETTING OF CONTROL PROBLEM 129 5.1.1 STATE-OBSERVATION SYSTEM
129 5.1.2 SET OF ADMISSIBLE CONTROLS 130 5.1.3 QUADRATIC COST FUNCTIONAL
131 5.2 SEPARATION PRINCIPLE 131 5.2.1 PROPERTIES OF ADMISSIBLE CONTROLS
132 5.2.2 EXTENDED SEPARATION PRINCIPLE 135 5.2.3 CLASSICAL SEPARATION
PRINCIPLE 137 5.2.4 PROOF OF LEMMA 5.15 138 5.3 GENERALIZATION TO A GAME
PROBLEM 139 5.3.1 SETTING OF GAME PROBLEM 139 5.3.2 CASE 1: THE FIRST
PLAYER HAS WORSE OBSERVATIONS 141 5.3.3 CASE 2: THE PLAYERS HAVE THE
SAME OBSERVATIONS 144 5.4 MINIMIZING SEQUENCE 145 5.4.1 PROPERTIES OF
COST FUNCTIONAL 145 5.4.2 MINIMIZING SEQUENCE 147 5.5 LINEAR REGULATOR
PROBLEM 148 5.5.1 SETTING OF LINEAR REGULATOR PROBLEM 148 5.5.2 OPTIMAL
REGULATOR 149 5.6 EXISTENCE OF OPTIMAL CONTROL 150 5.6.1 CONTROLS IN
LINEAR FEEDBACK FORM 150 5.6.2 EXISTENCE OF OPTIMAL CONTROL 151 5.6.3
APPLICATION TO EXISTENCE OF SADDLE POINTS 153 XII CONTENTS 5.7
CONCLUDING REMARKS 158 6 CONTROL AND ESTIMATION UNDER CORRELATED WHITE
NOISES 159 6.1 ESTIMATION: PRELIMINARIES 159 6.1.1 SETTING OF ESTIMATION
PROBLEMS 159 6.1.2 WIENER-HOPF EQUATION 160 6.2 FILTERING 162 6.2.1 DUAJ
LINEAR REGULATOR PROBLEM 162 6.2.2 OPTIMAL LINEAR FEEDBACK FILTER 164
6.2.3 ERROR PROCESS 166 6.2.4 INNOVATION PROCESS 168 6.3 PREDICTION 171
6.3.1 DUAL LINEAR REGULATOR PROBLEM 171 6.3.2 OPTIMAL LINEAR FEEDBACK
PREDICTOR 172 6.4 SMOOTHING 173 6.4.1 DUAL LINEAR REGULATOR PROBLEM 173
6.4.2 OPTIMAL LINEAR FEEDBACK SMOOTHER 174 6.5 STOCHASTIC REGULATOR
PROBLEM 177 6.5.1 SETTING OF THE PROBLEM 177 6.5.2 OPTIMAL STOCHASTIC
REGULATOR 178 7 CONTROL AND ESTIMATION UNDER COLORED NOISES 183 7.1
ESTIMATION 183 7.1.1 SETTING OF ESTIMATION PROBLEMS 183 7.1.2 REDUCTION
184 7.1.3 OPTIMAL LINEAR FEEDBACK ESTIMATORS 185 7.1.4 ABOUT THE RICCATI
EQUATION (7.15) 186 7.1.5 EXAMPLE: OPTIMAL FILTER IN DIFFERENTIAL FORM
189 7.2 STOCHASTIC REGULATOR PROBLEM 191 7.2.1 SETTING OF THE PROBLEM
191 7.2.2 REDUCTION 191 7.2.3 OPTIMAL STOCHASTIC REGULATOR 192 7.2.4
ABOUT THE RICCATI EQUATION (7.48) 193 7.2.5 EXAMPLE: OPTIMAL STOCHASTIC
REGULATOR IN DIFFERENTIAL FORM 196 8 CONTROL AND ESTIMATION UNDER WIDE
BAND NOISES 197 8.1 ESTIMATION 197 8.1.1 SETTING OF ESTIMATION PROBLEMS
197 8.1.2 THE FIRST REDUCTION 198 8.1.3 THE SECOND REDUCTION 201 8.1.4
OPTIMAL LINEAR FEEDBACK ESTIMATORS 206 8.1.5 ABOUT THE RICCATI EQUATION
(8.40) 207 8.1.6 EXAMPLE: OPTIMAL FILTER IN DIFFERENTIAL FORM 208
CONTENTS XIII 8.2 MORE ABOUT THE OPTIMAL FILTER 209 8.2.1 MORE ABOUT THE
RICCATI EQUATION (8.40) 210 8.2.2 EQUATIONS FOR THE OPTIMAL FILTER 216
8.3 STOCHASTIC REGULATOR PROBLEM 218 8.3.1 SETTING OF THE PROBLEM 218
8.3.2 REDUCTION 219 8.3.3 OPTIMAL STOCHASTIC REGULATOR 220 8.3.4 ABOUT
THE RICCATI EQUATION (8.81) 220 8.3.5 EXAMPLE: OPTIMAL STOCHASTIC
REGULATOR IN DIFFERENTIAL FORM 224 8.4 CONCLUDING REMARKS 225 9 CONTROL
AND ESTIMATION UNDER SHIFTED WHITE NOISES 227 9.1 PRELIMINARIES 227 9.2
STATE NOISE DELAYING OBSERVATION NOISE: FILTERING 230 9.2.1 SETTING OF
THE PROBLEM 230 9.2.2 DUAL LINEAR REGULATOR PROBLEM 231 9.2.3 OPTIMAL
LINEAR FEEDBACK FILTER 232 9.2.4 ABOUT THE RICCATI EQUATION (9.27) 235
9.2.5 ABOUT THE OPTIMAL FILTER 238 9.3 STATE NOISE DELAYING OBSERVATION
NOISE: PREDICTION 243 9.4 STATE NOISE DELAYING OBSERVATION NOISE:
SMOOTHING 247 9.5 STATE NOISE DELAYING OBSERVATION NOISE: STOCHASTIC
REGULATOR PROB- LEM 253 9.6 CONCLUDING REMARKS 255 10 CONTROL AND
ESTIMATION UNDER SHIFTED WHITE NOISES (REVISED) 257 10.1 PRELIMINARIES
257 10.2 SHIFTED WHITE NOISES AND BOUNDARY NOISES 259 10.3 CONVERGENCE
OF WIDE BAND NOISE PROCESSES 260 10.3.1 APPROXIMATION OF WHITE NOISES
260 10.3.2 APPROXIMATION OF SHIFTED WHITE NOISES 262 10.4 STATE NOISE
DELAYING OBSERVATION NOISE 264 10.4.1 SETTING OF THE PROBLEM 264 10.4.2
APPROXIMATING PROBLEMS 265 10.4.3 OPTIMAL CONTROL AND OPTIMAL FILTER 267
10.4.4 APPLICATION TO SPACE NAVIGATION AND GUIDANCE 271 10.5 STATE NOISE
ANTICIPATING OBSERVATION NOISE 275 10.5.1 SETTING OF THE PROBLEM 275
10.5.2 APPROXIMATING PROBLEMS 275 10.5.3 OPTIMAL CONTROL AND OPTIMAL
FILTER 276 XIV CONTENTS 11 DUALITY 279 11.1 CLASSICAL SEPARATION
PRINCIPLE AND DUALITY 279 11.2 EXTENDED SEPARATION PRINCIPLE AND DUALITY
281 11.3 INNOVATION PROCESS FOR CONTROL ACTIONS 283 12 CONTROLLABILITY
285 12.1 PRELIMINARIES 285 12.1.1 DEFINITIONS 285 12.1.2 DESCRIPTION OF
THE SYSTEM 289 12.2 CONTROLLABILITY: DETERMINISTIC SYSTEMS 290 12.2.1
CCC, ACC AND RANK CONDITION 290 12.2.2 RESOLVENT CONDITIONS 292 12.2.3
APPLICATIONS OF RESOLVENT CONDITIONS 295 12.3 CONTROLLABILITY:
STOCHASTIC SYSTEMS 300 12.3.1 ^-CONTROLLABILITY 300 12.3.2 C T
-CONTROLLABILITY 304 12.3.3 S T -CONTROLLABILITY 306 COMMENTS 311
BIBLIOGRAPHY 315 INDEX OF NOTATION 323 INDEX 329
|
| any_adam_object | 1 |
| author | Bashirov, Agamirza E. |
| author_GND | (DE-588)124392865 |
| author_facet | Bashirov, Agamirza E. |
| author_role | aut |
| author_sort | Bashirov, Agamirza E. |
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| bvnumber | BV023791639 |
| ctrlnum | (OCoLC)845550953 (DE-599)BVBBV023791639 |
| dewey-full | 003.74 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003.74 |
| dewey-search | 003.74 |
| dewey-sort | 13.74 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV023791639 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T21:37:11Z |
| institution | BVB |
| isbn | 376436999X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017433845 |
| oclc_num | 845550953 |
| open_access_boolean | |
| owner | DE-634 |
| owner_facet | DE-634 |
| physical | XXVI, 334 S. Ill. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Systems & Control |
| spellingShingle | Bashirov, Agamirza E. Partially observable linear systems under dependent noises Schätztheorie (DE-588)4121608-8 gnd Funktionalanalysis (DE-588)4018916-8 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd Lineares System (DE-588)4125617-7 gnd Stochastische optimale Kontrolle (DE-588)4207850-7 gnd |
| subject_GND | (DE-588)4121608-8 (DE-588)4018916-8 (DE-588)4207956-1 (DE-588)4125617-7 (DE-588)4207850-7 |
| title | Partially observable linear systems under dependent noises |
| title_auth | Partially observable linear systems under dependent noises |
| title_exact_search | Partially observable linear systems under dependent noises |
| title_full | Partially observable linear systems under dependent noises Agamirza E. Bashirov |
| title_fullStr | Partially observable linear systems under dependent noises Agamirza E. Bashirov |
| title_full_unstemmed | Partially observable linear systems under dependent noises Agamirza E. Bashirov |
| title_short | Partially observable linear systems under dependent noises |
| title_sort | partially observable linear systems under dependent noises |
| topic | Schätztheorie (DE-588)4121608-8 gnd Funktionalanalysis (DE-588)4018916-8 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd Lineares System (DE-588)4125617-7 gnd Stochastische optimale Kontrolle (DE-588)4207850-7 gnd |
| topic_facet | Schätztheorie Funktionalanalysis Unendlichdimensionales System Lineares System Stochastische optimale Kontrolle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017433845&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bashirovagamirzae partiallyobservablelinearsystemsunderdependentnoises |