Representation and control of infinite dimensional systems:
"The quadratic cost optimal control problem for systems described by linear ordinary differential equations occupies a central role in the study of control systems both from a theoretical and design point of view. The study of this problem over an infinite time horizon shows the beautiful inter...
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston ; Basel ; Berlin
Birkhäuser
2007
|
| Ausgabe: | second edition |
| Schriftenreihe: | Systems & control: foundations & applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Zusammenfassung: | "The quadratic cost optimal control problem for systems described by linear ordinary differential equations occupies a central role in the study of control systems both from a theoretical and design point of view. The study of this problem over an infinite time horizon shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability, observability, stabilizability, and detectability. This theory is far more difficult for infinite dimensional systems such as those with time delays and distributed parameter systems. ... Part I reviews basic optimal control and game theory of finite dimensional systems, which serves as an introduction to the book. Part II deals with time evolution of some generic controlled infinite dimensional systems and contains a fairly complete account of semigroup theory. It incorporates interpolation theory and exhibits the role of semigroup theory in delay differential and partial differential equations. Part III studies the generic qualitative properties of controlled systems. Parts IV and V examine the optimal control of systems when performance is measured via a quadratic cost. Boundary control of parabolic and hyperbolic systems and exact controllability are also covered"--P. [4] of cover. |
| Beschreibung: | xxvi, 575 Seiten Diagramme |
| ISBN: | 081764461X 9780817644611 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV022198026 | ||
| 003 | DE-604 | ||
| 005 | 20211105 | ||
| 007 | t | ||
| 008 | 061219s2007 |||| |||| 00||| eng d | ||
| 015 | |a 05,N44,0470 |2 dnb | ||
| 016 | 7 | |a 976672049 |2 DE-101 | |
| 020 | |a 081764461X |9 0-8176-4461-X | ||
| 020 | |a 9780817644611 |9 978-0-8176-4461-1 | ||
| 024 | 3 | |a 9780817644611 | |
| 028 | 5 | 2 | |a 11424666 |
| 035 | |a (OCoLC)74650361 | ||
| 035 | |a (DE-599)BVBBV022198026 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-703 |a DE-11 |a DE-29T |a DE-739 |a DE-83 | ||
| 050 | 0 | |a QA402.3 | |
| 082 | 0 | |a 629.8/312 |2 22 | |
| 084 | |a SK 880 |0 (DE-625)143266: |2 rvk | ||
| 084 | |a 34G10 |2 msc | ||
| 084 | |a 510 |2 sdnb | ||
| 084 | |a 47D06 |2 msc | ||
| 084 | |a 93C35 |2 msc | ||
| 084 | |a 47N70 |2 msc | ||
| 084 | |a 34H05 |2 msc | ||
| 084 | |a 93C95 |2 msc | ||
| 100 | 1 | |a Bensoussan, Alain |d 1940- |0 (DE-588)13295947X |4 aut | |
| 245 | 1 | 0 | |a Representation and control of infinite dimensional systems |c Bensoussan, Alain; Da Prato, Giuseppe; Delfour, Michel C.; Mitter, Sanjoy K. |
| 250 | |a second edition | ||
| 264 | 1 | |a Boston ; Basel ; Berlin |b Birkhäuser |c 2007 | |
| 300 | |a xxvi, 575 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Systems & control: foundations & applications | |
| 520 | 3 | |a "The quadratic cost optimal control problem for systems described by linear ordinary differential equations occupies a central role in the study of control systems both from a theoretical and design point of view. The study of this problem over an infinite time horizon shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability, observability, stabilizability, and detectability. This theory is far more difficult for infinite dimensional systems such as those with time delays and distributed parameter systems. ... Part I reviews basic optimal control and game theory of finite dimensional systems, which serves as an introduction to the book. Part II deals with time evolution of some generic controlled infinite dimensional systems and contains a fairly complete account of semigroup theory. It incorporates interpolation theory and exhibits the role of semigroup theory in delay differential and partial differential equations. Part III studies the generic qualitative properties of controlled systems. Parts IV and V examine the optimal control of systems when performance is measured via a quadratic cost. Boundary control of parabolic and hyperbolic systems and exact controllability are also covered"--P. [4] of cover. | |
| 650 | 4 | |a Commande, Théorie de la | |
| 650 | 4 | |a Optimisation mathématique | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 0 | 7 | |a Unendlichdimensionales System |0 (DE-588)4207956-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kontrolltheorie |0 (DE-588)4032317-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineare Differentialgleichung |0 (DE-588)4206889-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Unendlichdimensionales System |0 (DE-588)4207956-1 |D s |
| 689 | 0 | 1 | |a Lineare Differentialgleichung |0 (DE-588)4206889-7 |D s |
| 689 | 0 | 2 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Unendlichdimensionales System |0 (DE-588)4207956-1 |D s |
| 689 | 1 | 1 | |a Kontrolltheorie |0 (DE-588)4032317-1 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Da Prato, Giuseppe |d 1936-2023 |0 (DE-588)121352641 |4 aut | |
| 700 | 1 | |a Delfour, Michel C. |d 1943- |0 (DE-588)17252931X |4 aut | |
| 700 | 1 | |a Mitter, Sanjoy K. |d 1933- |0 (DE-588)122995430 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-8176-4581-6 |
| 856 | 4 | 2 | |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=2687851&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015409501&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-015409501 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804136173454491648 |
|---|---|
| adam_text | ALAIN BENSOUSSAN GIUSEPPE DA PRATO MICHEL C. DELFOUR SANJOY K. MITTER
REPRESENTATION AND CONTROL OF INFINITE DIMENSIONAL SYSTEMS SECOND
EDITION BIRKHAEUSER BOSTON * BASEL * BERLIN CONTENTS PREFACE TO THE
SECOND EDITION VII A NEW EDITION IN A SINGLE VOLUME VII DESCRIPTION OF
THE FIVE PARTS VIII ACKNOWLEDGMENTS X PREFACE TO VOLUME I OF THE FIRST
EDITION XI PREFACE TO VOLUME II OF THE FIRST EDITION XV LIST OF FIGURES
XXVII INTRODUCTION 1 1 SCOPE OF THE BOOK 1 2 FROM FINITE TO INFINITE
DIMENSIONAL SYTEMS 2 NOTES: SOME RELATED BOOKS ON THE CONTROL OF LINEAR
SYSTEMS THAT HAVE APPEARED SINCE 1992 10 PART I FINITE DIMENSIONAL
LINEAR CONTROL DYNAMICAL SYSTEMS 1 CONTROL OF LINEAR DIFFERENTIAL
SYSTEMS 13 1 INTRODUCTION 13 2 CONTROLLABILITY, OBSERVABILITY,
STABILIZABILITY, AND DETECTABILITY 13 2.1 CONTROLLABILITY 14 2.2
OBSERVABILITY 18 2.3 DUALITY 19 2.4 CANONICAL STRUCTURE FOR LINEAR
SYSTEMS 20 2.5 THE POLE-ASSIGNMENT THEOREM 20 2.6 STABILIZABILITY AND
DETECTABILITY 23 2.7 APPLICATIONS OF CONTROLLABILITY AND OBSERVABILITY
25 3 OPTIMAL CONTROL 30 XX CONTENTS 3.1 FINITE TIME HORIZON 30 3.2
INFINITE TIME HORIZON 33 4 A GLIMPSE INTO IJ-THEORY: STATE FEEDBACK
CASE 35 4.1 INTRODUCTION 35 4.2 MAIN RESULTS 36 5 DISSIPATIVE SYSTEMS 39
5.1 DEFINITIONS AND PRELIMINARY RESULTS 39 5.2 ASSOCIATED VARIATIONAL
PROBLEMS 40 5.3 QUADRATIC STORAGE FUNCTIONS 43 6 FINAL REMARKS 44 NOTES
44 2 LINEAR QUADRATIC TWO-PERSON ZERO-SUM DIFFERENTIAL GAMES 47 1
INTRODUCTION 47 2 DEFINITIONS, NOTATION, AND PRELIMINARY RESULTS 50 2.1
SYSTEM, UTILITY FUNCTION, AND VALUES OF THE GAME 50 2.2 PROPERTIES,
SEMI-DERIVATIVES, AND CONVEXITY/CONCAVITY OF C XO (U, V) 52 3 SADDLE
POINT AND COUPLED STATE-ADJOINT STATE SYSTEM 54 4 FINITE OPEN LOOP LOWER
VALUE 56 4.1 MAIN THEOREMS 56 4.2 ABSTRACT OPERATORS AND A PRELIMINARY
LEMMA 57 4.3 EXISTENCE AND CHARACTERIZATION OF THE MINIMIZERS .... 59
4.4 INTERMEDIARY RESULTS 62 4.5 EXISTENCE AND CHARACTERIZATION OF
MAXIMIZERS OF THE MINIMUM 64 4.6 FINITE OPEN LOOP LOWER VALUE FOR ALL
INITIAL STATES AND UNIQUENESS OF SOLUTION OF THE COUPLED SYSTEM 66 5
FINITE OPEN LOOP VALUE AND OPEN LOOP SADDLE POINT 68 6 RICCATI
DIFFERENTIAL EQUATION IN THE OPEN LOOP SADDLE POINT CASE 69 6.1
INVARIANT EMBEDDING WITH RESPECT TO THE INITIAL TIME . 69 6.2 FROM
CONVEXITY/CONCAVITY IN [0, T] TO [S, T] 70 6.3 OPEN LOOP SADDLE POINT
OPTIMALITY PRINCIPLE 71 6.4 DECOUPLING OF THE COUPLED SYSTEM 75 6.5
RICCATI DIFFERENTIAL EQUATION 77 6.6 OPEN LOOP SADDLE POINT AND RICCATI
DIFFERENTIAL EQUATION 78 6.7 THE GENERAL CASE OF REMARK 2.1 80 7 RICCATI
DIFFERENTIAL EQUATION AND OPEN/CLOSED LOOP UPPER/LOWER VALUE OF THE GAME
81 CONTENTS XXI PART II REPRESENTATION OF INFINITE DIMENSIONAL LINEAR
CONTROL DYNAMICAL SYSTEMS 1 SEMIGROUPS OF OPERATORS AND INTERPOLATION 87
1 NOTATION 87 2 LINEAR EVOLUTION EQUATIONS AND STRONGLY CONTINUOUS
SEMIGROUPS 88 2.1 DEFINITIONS AND PRELIMINARY RESULTS 88 2.2 ASYMPTOTIC
BEHAVIOR OF S(T) 91 2.3 SPECTRAL PROPERTIES OF THE INFINITESIMAL
GENERATOR .... 100 2.4 HILLE-YOSIDA-MIYADERA-FELLER-PHILLIPS THEOREM 101
2.5 ADJOINT SEMIGROUPS AND THEIR GENERATORS 103 2.6 SEMIGROUPS OF
CONTRACTIONS AND DISSIPATIVE OPERATORS . 104 2.7 ANALYTIC SEMIGROUPS 108
2.8 DIFFERENTIABLE SEMIGROUPS 115 2.9 SPECTRAL DETERMINING GROWTH
CONDITION 119 2.10 EXAMPLES OF SEMIGROUPS 122 3 NONHOMOGENEOUS LINEAR
EVOLUTION EQUATIONS 128 3.1 SETTING OF THE PROBLEM AND DEFINITIONS 128
3.2 EXISTENCE AND UNIQUENESS OF A STRONG SOLUTION 130 3.3 EXISTENCE OF A
STRICT SOLUTION 133 3.4 PERTURBATIONS OF INFINITESIMAL GENERATORS 134
3.5 EVOLUTION OPERATORS 138 3.6 MAXIMAL REGULARITY RESULTS IN HILBERT
SPACES AND MAIN ISOMORPHISM 139 3.7 REGULARITY RESULTS IN C([0, T];X)
146 3.8 EXAMPLES OF NONHOMOGENEOUS PROBLEMS 148 3.9 POINT SPECTRUM
OPERATORS 151 4 INTERPOLATION SPACES 154 4.1 NOTATION 154 4.2 SPACES OF
TRACES T(P, A, X 0 , X{) 154 4.3 SPACES OF AVERAGES (X 0 , XI)G }P 159
4.4 INTERPOLATION SPACES BETWEEN THE DOMAIN OF A LINEAR OPERATOR A AND
THE SPACE X 162 4.5 THE CASE OF A STRONGLY CONTINUOUS SEMIGROUP 163 4.6
THE CASE OF AN ANALYTIC SEMIGROUP 164 4.7 THE INTERPOLATION SPACE [X,
Y]G 166 5 FRACTIONAL POWERS OF DISSIPATIVE OPERATORS 167 6 INTERPOLATION
SPACES AND DOMAINS OF FRACTIONAL POWERS OF AN OPERATOR 169 XXII CONTENTS
2 VARIATIONAL THEORY OF PARABOLIC SYSTEMS 173 1 VARIATIONAL DIFFERENTIAL
EQUATIONS 173 1.1 DISTRIBUTED CONTROL 173 1.2 BOUNDARY CONTROL CONDITION
176 1.3 MAIN THEOREM 177 1.4 A PERTURBATION THEOREM 179 1.5 A REGULARITY
THEOREM 180 2 METHOD OF TRANSPOSITION 188 2.1 CONTROL THROUGH A
DIRICHLET BOUNDARY CONDITION 188 2.2 POINT CONTROL 190 2.3 MAIN RESULT
191 2.4 APPLICATION OF TRANSPOSITION TO THE EXAMPLES OF §2.1 AND §2.2
192 2.5 A CHANGE OF VARIABLE 196 2.6 OTHER ISOMORPHISMS 198 3 SECOND
ORDER PROBLEMS 198 3 SEMIGROUP METHODS FOR SYSTEMS WITH UNBOUNDED
CONTROL AND OBSERVATION OPERATORS 201 1 COMPLEMENTS ON SEMIGROUPS 201
1.1 NOTATION 201 2 COMPLEMENTS ON ANALYTIC SEMIGROUPS 206 2.1 REGULARITY
RESULTS 207 2.2 OTHER REPRESENTATIONS AND THE METHOD OF CHANGE OF
VARIABLE 209 3 UNBOUNDED CONTROL AND OBSERVATION OPERATORS 210 3.1
ANALYTIC SYSTEMS 211 3.2 UNBOUNDED CONTROL OPERATORS 212 3.3 UNBOUNDED
OBSERVATION OPERATORS 216 3.4 UNBOUNDED CONTROL AND OBSERVATION
OPERATORS 218 4 TIME-INVARIANT VARIATIONAL PARABOLIC SYSTEMS 222 4 STATE
SPACE THEORY OF DIFFERENTIAL SYSTEMS WITH DELAYS . 229 1 INTRODUCTION
229 2 EXAMPLES AND ORIENTATION 231 2.1 EXAMPLES 231 2.2 ORIENTATION 235
2.3 NOTATION 238 3 EXISTENCE THEOREMS FOR LIPSCHITZIAN SYSTEMS 240 3.1
CONTINUOUS FUNCTIONS FRAMEWORK 240 3.2 L P OR PRODUCT SPACE FRAMEWORK
245 3.3 LINEAR TIME-INVARIANT SYSTEMS 249 4 STATE SPACE THEORY OF LINEAR
TIME-INVARIANT SYSTEMS 252 4.1 PRELIMINARY RESULTS AND SMOOTHNESS OF THE
SOLUTION .. 252 4.2 FIRST STATE EQUATION 254 CONTENTS XXIII 4.3
TRANSPOSED AND ADJOINT SYSTEMS 260 4.4 STRUCTURAL OPERATORS 263 4.5
ADJOINT SEMIGROUP {S T *(T)} AND INTERTWINING THEOREMS 265 4.6
INFINITESIMAL GENERATORS A T * AND A* 269 4.7 THE COMPANION STRUCTURAL
OPERATOR G OF F 275 5 STATE SPACE THEORY OF LINEAR CONTROL SYSTEMS 279
5.1 THE STRUCTURAL STATE 280 5.2 THE EXTENDED STATE 286 6 STATE SPACE
THEORY OF LINEAR CONTROL SYSTEMS WITH OBSERVATION 297 6.1 THE EXTENDED
STATE 299 6.2 THE EXTENDED STRUCTURAL STATE 300 6.3 INTERTWINING
PROPERTY OF THE TWO EXTENDED STATES 308 PART III QUALITATIVE PROPERTIES
OF INFINITE DIMENSIONAL LINEAR CONTROL DYNAMICAL SYSTEMS 1
CONTROLLABILITY AND OBSERVABILITY FOR A CLASS OF INFINITE DIMENSIONAL
SYSTEMS 313 1 INTRODUCTION 313 2 MAIN DEFINITIONS 317 2.1 NOTATION 317
2.2 DEFINITIONS 318 3 CRITERIA FOR APPROXIMATE AND EXACT CONTROLLABILITY
322 3.1 CRITERION FOR APPROXIMATE CONTROLLABILITY 322 3.2 CRITERIA FOR
EXACT CONTROLLABILITY AND CONTINUOUS OBSERVABILITY 323 3.3 APPROXIMATION
324 4 FINITE DIMENSIONAL CONTROL SPACE 325 4.1 FINITE DIMENSIONAL CASE
325 4.2 GENERAL STATE SPACE 328 5 CONTROLLABILITY FOR THE HEAT EQUATION
330 5.1 DISTRIBUTED CONTROL 330 5.2 BOUNDARY CONTROL 331 5.3 NEUMANN
BOUNDARY CONTROL 334 5.4 POINTWISE CONTROL 338 6 CONTROLLABILITY FOR
SKEW-SYMMETRIC OPERATORS 339 6.1 NOTATION AND GENERAL COMMENTS 339 6.2
DYNAMICAL SYSTEM 342 6.3 APPROXIMATION 352 6.4 EXACT CONTROLLABILITY FOR
T ARBITRARILY SMALL 357 7 GENERAL FRAMEWORK: SKEW-SYMMETRIC OPERATORS
362 7.1 OPERATOR A 362 7.2 OPERATOR * 363 XXIV CONTENTS 7.3 DYNAMICAL
SYSTEM 364 7.4 EXACT CONTROLLABILITY 365 8 EXACT CONTROLLABILITY OF
HYPERBOLIC EQUATIONS 367 8.1 WAVE EQUATION WITH DIRICHLET BOUNDARY
CONTROL 368 8.2 WAVE EQUATION WITH NEUMANN BOUNDARY CONTROL 369 8.3
MAXWELL EQUATIONS 371 8.4 PLATE EQUATION 377 PART IV QUADRATIC OPTIMAL
CONTROL: FINITE TIME HORIZON 1 BOUNDED CONTROL OPERATORS: CONTROL INSIDE
THE DOMAIN . 385 1 INTRODUCTION AND SETTING OF THE PROBLEM 385 2
SOLUTION OF THE RICCATI EQUATION 386 2.1 NOTATION AND PRELIMINARIES 386
2.2 RICCATI EQUATION 390 2.3 REPRESENTATION FORMULAS FOR THE SOLUTION OF
THE RICCATI EQUATION 395 3 STRICT AND CLASSICAL SOLUTIONS OF THE RICCATI
EQUATION 397 3.1 THE GENERAL CASE 398 3.2 THE ANALYTIC CASE 400 3.3 THE
VARIATIONAL CASE 403 4 THE CASE OF THE UNBOUNDED OBSERVATION 405 4.1 THE
ANALYTIC CASE 407 4.2 THE VARIATIONAL CASE 407 5 THE CASE WHEN A
GENERATES A GROUP 407 6 THE LINEAR QUADRATIC CONTROL PROBLEM WITH FINITE
HORIZON .... 408 6.1 THE MAIN RESULT 408 6.2 THE CASE OF UNBOUNDED
OBSERVATION 410 6.3 REGULARITY PROPERTIES OF THE OPTIMAL CONTROL 411 6.4
HAMILTONIAN SYSTEMS 412 7 SOME GENERALIZATIONS AND COMPLEMENTS 412 7.1
NONHOMOGENEOUS STATE EQUATION 412 7.2 TIME-DEPENDENT STATE EQUATION AND
COST FUNCTION .... 414 7.3 DUAL RICCATI EQUATION 416 8 EXAMPLES OF
CONTROLLED SYSTEMS 418 8.1 PARABOLIC EQUATIONS 418 8.2 WAVE EQUATION 420
8.3 DELAY EQUATIONS 423 8.4 EVOLUTION EQUATIONS IN NONCYLINDRICAL
DOMAINS 428 CONTENTS XXV 2 UNBOUNDED CONTROL OPERATORS: PARABOLIC
EQUATIONS WITH CONTROL ON THE BOUNDARY 431 1 INTRODUCTION 431 2 RICCATI
EQUATION 438 2.1 NOTATION 438 2.2 RICCATI EQUATION FOR A 1/2 439 2.3
SOLUTION OF THE RICCATI EQUATION FOR A 1/2 446 3 DYNAMIC PROGRAMMING
454 3 UNBOUNDED CONTROL OPERATORS: HYPERBOLIC EQUATIONS WITH CONTROL ON
THE BOUNDARY 459 1 INTRODUCTION 459 2 RICCATI EQUATION 462 3 DYNAMIC
PROGRAMMING 463 4 EXAMPLES OF CONTROLLED HYPERBOLIC SYSTEMS 466 5 SOME
RESULT FOR GENERAL SEMIGROUPS 471 PART V QUADRATIC OPTIMAL CONTROL:
INFINITE TIME HORIZON 1 BOUNDED CONTROL OPERATORS: CONTROL INSIDE THE
DOMAIN . 479 1 INTRODUCTION AND SETTING OF THE PROBLEM 479 2 THE
ALGEBRAIC RICCATI EQUATION 480 3 SOLUTION OF THE CONTROL PROBLEM 486 3.1
FEEDBACK OPERATOR AND DETECTABILITY 487 3.2 STABILIZABILITY AND
STABILITY OF THE CLOSED LOOP OPERATOR F IN THE POINT SPECTRUM CASE 489
3.3 STABILIZABILITY 490 3.4 EXPONENTIAL STABILITY OF F 492 4 QUALITATIVE
PROPERTIES OF THE SOLUTIONS OF THE RICCATI EQUATION 493 4.1 LOCAL
STABILITY RESULTS 494 4.2 ATTRACTIVITY PROPERTIES OF A STATIONARY
SOLUTION 495 4.3 MAXIMAL SOLUTIONS 497 4.4 CONTINUOUS DEPENDENCE OF
STATIONARY SOLUTIONS WITH RESPECT TO THE DATA 501 4.5 PERIODIC SOLUTIONS
OF THE RICCATI EQUATION 502 5 SOME GENERALIZATIONS AND COMPLEMENTS 505
5.1 NONHOMOGENEOUS STATE EQUATION 505 5.2 TIME-DEPENDENT STATE EQUATION
AND COST FUNCTION .... 507 5.3 PERIODIC CONTROL PROBLEMS 509 6 EXAMPLES
OF CONTROLLED SYSTEMS 513 6.1 PARABOLIC EQUATIONS 513 6.2 WAVE EQUATION
514 6.3 STRONGLY DAMPED WAVE EQUATION 515 XXVI CONTENTS 2 UNBOUNDED
CONTROL OPERATORS: PARABOLIC EQUATIONS WITH CONTROL ON THE BOUNDARY 517
1 INTRODUCTION AND SETTING OF THE PROBLEM 517 2 THE ALGEBRAIC RICCATI
EQUATION 518 3 DYNAMIC PROGRAMMING 521 3.1 EXISTENCE AND UNIQUENESS OF
THE OPTIMAL CONTROL 521 3.2 FEEDBACK OPERATOR AND DETECTABILITY 523 3.3
STABILIZABILITY AND STABILITY OF F IN THE POINT SPECTRUM CASE 525 3
UNBOUNDED CONTROL OPERATORS: HYPERBOLIC EQUATIONS WITH CONTROL ON THE
BOUNDARY 529 1 INTRODUCTION AND SETTING OF THE PROBLEM 529 2 MAIN
RESULTS 530 3 SOME RESULT FOR GENERAL SEMIGROUPS 534 A AN ISOMORPHISM
RESULT 537 REFERENCES 541 INDEX 569
|
| adam_txt |
ALAIN BENSOUSSAN GIUSEPPE DA PRATO MICHEL C. DELFOUR SANJOY K. MITTER
REPRESENTATION AND CONTROL OF INFINITE DIMENSIONAL SYSTEMS SECOND
EDITION BIRKHAEUSER BOSTON * BASEL * BERLIN CONTENTS PREFACE TO THE
SECOND EDITION VII A NEW EDITION IN A SINGLE VOLUME VII DESCRIPTION OF
THE FIVE PARTS VIII ACKNOWLEDGMENTS X PREFACE TO VOLUME I OF THE FIRST
EDITION XI PREFACE TO VOLUME II OF THE FIRST EDITION XV LIST OF FIGURES
XXVII INTRODUCTION 1 1 SCOPE OF THE BOOK 1 2 FROM FINITE TO INFINITE
DIMENSIONAL SYTEMS 2 NOTES: SOME RELATED BOOKS ON THE CONTROL OF LINEAR
SYSTEMS THAT HAVE APPEARED SINCE 1992 10 PART I FINITE DIMENSIONAL
LINEAR CONTROL DYNAMICAL SYSTEMS 1 CONTROL OF LINEAR DIFFERENTIAL
SYSTEMS 13 1 INTRODUCTION 13 2 CONTROLLABILITY, OBSERVABILITY,
STABILIZABILITY, AND DETECTABILITY 13 2.1 CONTROLLABILITY 14 2.2
OBSERVABILITY 18 2.3 DUALITY 19 2.4 CANONICAL STRUCTURE FOR LINEAR
SYSTEMS 20 2.5 THE POLE-ASSIGNMENT THEOREM 20 2.6 STABILIZABILITY AND
DETECTABILITY 23 2.7 APPLICATIONS OF CONTROLLABILITY AND OBSERVABILITY
25 3 OPTIMAL CONTROL 30 XX CONTENTS 3.1 FINITE TIME HORIZON 30 3.2
INFINITE TIME HORIZON 33 4 A GLIMPSE INTO IJ-THEORY: STATE FEEDBACK
CASE 35 4.1 INTRODUCTION 35 4.2 MAIN RESULTS 36 5 DISSIPATIVE SYSTEMS 39
5.1 DEFINITIONS AND PRELIMINARY RESULTS 39 5.2 ASSOCIATED VARIATIONAL
PROBLEMS 40 5.3 QUADRATIC STORAGE FUNCTIONS 43 6 FINAL REMARKS 44 NOTES
44 2 LINEAR QUADRATIC TWO-PERSON ZERO-SUM DIFFERENTIAL GAMES 47 1
INTRODUCTION 47 2 DEFINITIONS, NOTATION, AND PRELIMINARY RESULTS 50 2.1
SYSTEM, UTILITY FUNCTION, AND VALUES OF THE GAME 50 2.2 PROPERTIES,
SEMI-DERIVATIVES, AND CONVEXITY/CONCAVITY OF C XO (U, V) 52 3 SADDLE
POINT AND COUPLED STATE-ADJOINT STATE SYSTEM 54 4 FINITE OPEN LOOP LOWER
VALUE 56 4.1 MAIN THEOREMS 56 4.2 ABSTRACT OPERATORS AND A PRELIMINARY
LEMMA 57 4.3 EXISTENCE AND CHARACTERIZATION OF THE MINIMIZERS . 59
4.4 INTERMEDIARY RESULTS 62 4.5 EXISTENCE AND CHARACTERIZATION OF
MAXIMIZERS OF THE MINIMUM 64 4.6 FINITE OPEN LOOP LOWER VALUE FOR ALL
INITIAL STATES AND UNIQUENESS OF SOLUTION OF THE COUPLED SYSTEM 66 5
FINITE OPEN LOOP VALUE AND OPEN LOOP SADDLE POINT 68 6 RICCATI
DIFFERENTIAL EQUATION IN THE OPEN LOOP SADDLE POINT CASE 69 6.1
INVARIANT EMBEDDING WITH RESPECT TO THE INITIAL TIME . 69 6.2 FROM
CONVEXITY/CONCAVITY IN [0, T] TO [S, T] 70 6.3 OPEN LOOP SADDLE POINT
OPTIMALITY PRINCIPLE 71 6.4 DECOUPLING OF THE COUPLED SYSTEM 75 6.5
RICCATI DIFFERENTIAL EQUATION 77 6.6 OPEN LOOP SADDLE POINT AND RICCATI
DIFFERENTIAL EQUATION 78 6.7 THE GENERAL CASE OF REMARK 2.1 80 7 RICCATI
DIFFERENTIAL EQUATION AND OPEN/CLOSED LOOP UPPER/LOWER VALUE OF THE GAME
81 CONTENTS XXI PART II REPRESENTATION OF INFINITE DIMENSIONAL LINEAR
CONTROL DYNAMICAL SYSTEMS 1 SEMIGROUPS OF OPERATORS AND INTERPOLATION 87
1 NOTATION 87 2 LINEAR EVOLUTION EQUATIONS AND STRONGLY CONTINUOUS
SEMIGROUPS 88 2.1 DEFINITIONS AND PRELIMINARY RESULTS 88 2.2 ASYMPTOTIC
BEHAVIOR OF S(T) 91 2.3 SPECTRAL PROPERTIES OF THE INFINITESIMAL
GENERATOR . 100 2.4 HILLE-YOSIDA-MIYADERA-FELLER-PHILLIPS THEOREM 101
2.5 ADJOINT SEMIGROUPS AND THEIR GENERATORS 103 2.6 SEMIGROUPS OF
CONTRACTIONS AND DISSIPATIVE OPERATORS . 104 2.7 ANALYTIC SEMIGROUPS 108
2.8 DIFFERENTIABLE SEMIGROUPS 115 2.9 SPECTRAL DETERMINING GROWTH
CONDITION 119 2.10 EXAMPLES OF SEMIGROUPS 122 3 NONHOMOGENEOUS LINEAR
EVOLUTION EQUATIONS 128 3.1 SETTING OF THE PROBLEM AND DEFINITIONS 128
3.2 EXISTENCE AND UNIQUENESS OF A STRONG SOLUTION 130 3.3 EXISTENCE OF A
STRICT SOLUTION 133 3.4 PERTURBATIONS OF INFINITESIMAL GENERATORS 134
3.5 EVOLUTION OPERATORS 138 3.6 MAXIMAL REGULARITY RESULTS IN HILBERT
SPACES AND MAIN ISOMORPHISM 139 3.7 REGULARITY RESULTS IN C([0, T];X)
146 3.8 EXAMPLES OF NONHOMOGENEOUS PROBLEMS 148 3.9 POINT SPECTRUM
OPERATORS 151 4 INTERPOLATION SPACES 154 4.1 NOTATION 154 4.2 SPACES OF
TRACES T(P, A, X 0 , X{) 154 4.3 SPACES OF AVERAGES (X 0 , XI)G }P 159
4.4 INTERPOLATION SPACES BETWEEN THE DOMAIN OF A LINEAR OPERATOR A AND
THE SPACE X 162 4.5 THE CASE OF A STRONGLY CONTINUOUS SEMIGROUP 163 4.6
THE CASE OF AN ANALYTIC SEMIGROUP 164 4.7 THE INTERPOLATION SPACE [X,
Y]G 166 5 FRACTIONAL POWERS OF DISSIPATIVE OPERATORS 167 6 INTERPOLATION
SPACES AND DOMAINS OF FRACTIONAL POWERS OF AN OPERATOR 169 XXII CONTENTS
2 VARIATIONAL THEORY OF PARABOLIC SYSTEMS 173 1 VARIATIONAL DIFFERENTIAL
EQUATIONS 173 1.1 DISTRIBUTED CONTROL 173 1.2 BOUNDARY CONTROL CONDITION
176 1.3 MAIN THEOREM 177 1.4 A PERTURBATION THEOREM 179 1.5 A REGULARITY
THEOREM 180 2 METHOD OF TRANSPOSITION 188 2.1 CONTROL THROUGH A
DIRICHLET BOUNDARY CONDITION 188 2.2 POINT CONTROL 190 2.3 MAIN RESULT
191 2.4 APPLICATION OF TRANSPOSITION TO THE EXAMPLES OF §2.1 AND §2.2
192 2.5 A CHANGE OF VARIABLE 196 2.6 OTHER ISOMORPHISMS 198 3 SECOND
ORDER PROBLEMS 198 3 SEMIGROUP METHODS FOR SYSTEMS WITH UNBOUNDED
CONTROL AND OBSERVATION OPERATORS 201 1 COMPLEMENTS ON SEMIGROUPS 201
1.1 NOTATION 201 2 COMPLEMENTS ON ANALYTIC SEMIGROUPS 206 2.1 REGULARITY
RESULTS 207 2.2 OTHER REPRESENTATIONS AND THE METHOD OF CHANGE OF
VARIABLE 209 3 UNBOUNDED CONTROL AND OBSERVATION OPERATORS 210 3.1
ANALYTIC SYSTEMS 211 3.2 UNBOUNDED CONTROL OPERATORS 212 3.3 UNBOUNDED
OBSERVATION OPERATORS 216 3.4 UNBOUNDED CONTROL AND OBSERVATION
OPERATORS 218 4 TIME-INVARIANT VARIATIONAL PARABOLIC SYSTEMS 222 4 STATE
SPACE THEORY OF DIFFERENTIAL SYSTEMS WITH DELAYS . 229 1 INTRODUCTION
229 2 EXAMPLES AND ORIENTATION 231 2.1 EXAMPLES 231 2.2 ORIENTATION 235
2.3 NOTATION 238 3 EXISTENCE THEOREMS FOR LIPSCHITZIAN SYSTEMS 240 3.1
CONTINUOUS FUNCTIONS FRAMEWORK 240 3.2 L P OR PRODUCT SPACE FRAMEWORK
245 3.3 LINEAR TIME-INVARIANT SYSTEMS 249 4 STATE SPACE THEORY OF LINEAR
TIME-INVARIANT SYSTEMS 252 4.1 PRELIMINARY RESULTS AND SMOOTHNESS OF THE
SOLUTION . 252 4.2 FIRST STATE EQUATION 254 CONTENTS XXIII 4.3
TRANSPOSED AND ADJOINT SYSTEMS 260 4.4 STRUCTURAL OPERATORS 263 4.5
ADJOINT SEMIGROUP {S T *(T)} AND INTERTWINING THEOREMS 265 4.6
INFINITESIMAL GENERATORS A T * AND A* 269 4.7 THE COMPANION STRUCTURAL
OPERATOR G OF F 275 5 STATE SPACE THEORY OF LINEAR CONTROL SYSTEMS 279
5.1 THE STRUCTURAL STATE 280 5.2 THE EXTENDED STATE 286 6 STATE SPACE
THEORY OF LINEAR CONTROL SYSTEMS WITH OBSERVATION 297 6.1 THE EXTENDED
STATE 299 6.2 THE EXTENDED STRUCTURAL STATE 300 6.3 INTERTWINING
PROPERTY OF THE TWO EXTENDED STATES 308 PART III QUALITATIVE PROPERTIES
OF INFINITE DIMENSIONAL LINEAR CONTROL DYNAMICAL SYSTEMS 1
CONTROLLABILITY AND OBSERVABILITY FOR A CLASS OF INFINITE DIMENSIONAL
SYSTEMS 313 1 INTRODUCTION 313 2 MAIN DEFINITIONS 317 2.1 NOTATION 317
2.2 DEFINITIONS 318 3 CRITERIA FOR APPROXIMATE AND EXACT CONTROLLABILITY
322 3.1 CRITERION FOR APPROXIMATE CONTROLLABILITY 322 3.2 CRITERIA FOR
EXACT CONTROLLABILITY AND CONTINUOUS OBSERVABILITY 323 3.3 APPROXIMATION
324 4 FINITE DIMENSIONAL CONTROL SPACE 325 4.1 FINITE DIMENSIONAL CASE
325 4.2 GENERAL STATE SPACE 328 5 CONTROLLABILITY FOR THE HEAT EQUATION
330 5.1 DISTRIBUTED CONTROL 330 5.2 BOUNDARY CONTROL 331 5.3 NEUMANN
BOUNDARY CONTROL 334 5.4 POINTWISE CONTROL 338 6 CONTROLLABILITY FOR
SKEW-SYMMETRIC OPERATORS 339 6.1 NOTATION AND GENERAL COMMENTS 339 6.2
DYNAMICAL SYSTEM 342 6.3 APPROXIMATION 352 6.4 EXACT CONTROLLABILITY FOR
T ARBITRARILY SMALL 357 7 GENERAL FRAMEWORK: SKEW-SYMMETRIC OPERATORS
362 7.1 OPERATOR A 362 7.2 OPERATOR * 363 XXIV CONTENTS 7.3 DYNAMICAL
SYSTEM 364 7.4 EXACT CONTROLLABILITY 365 8 EXACT CONTROLLABILITY OF
HYPERBOLIC EQUATIONS 367 8.1 WAVE EQUATION WITH DIRICHLET BOUNDARY
CONTROL 368 8.2 WAVE EQUATION WITH NEUMANN BOUNDARY CONTROL 369 8.3
MAXWELL EQUATIONS 371 8.4 PLATE EQUATION 377 PART IV QUADRATIC OPTIMAL
CONTROL: FINITE TIME HORIZON 1 BOUNDED CONTROL OPERATORS: CONTROL INSIDE
THE DOMAIN . 385 1 INTRODUCTION AND SETTING OF THE PROBLEM 385 2
SOLUTION OF THE RICCATI EQUATION 386 2.1 NOTATION AND PRELIMINARIES 386
2.2 RICCATI EQUATION 390 2.3 REPRESENTATION FORMULAS FOR THE SOLUTION OF
THE RICCATI EQUATION 395 3 STRICT AND CLASSICAL SOLUTIONS OF THE RICCATI
EQUATION 397 3.1 THE GENERAL CASE 398 3.2 THE ANALYTIC CASE 400 3.3 THE
VARIATIONAL CASE 403 4 THE CASE OF THE UNBOUNDED OBSERVATION 405 4.1 THE
ANALYTIC CASE 407 4.2 THE VARIATIONAL CASE 407 5 THE CASE WHEN A
GENERATES A GROUP 407 6 THE LINEAR QUADRATIC CONTROL PROBLEM WITH FINITE
HORIZON . 408 6.1 THE MAIN RESULT 408 6.2 THE CASE OF UNBOUNDED
OBSERVATION 410 6.3 REGULARITY PROPERTIES OF THE OPTIMAL CONTROL 411 6.4
HAMILTONIAN SYSTEMS 412 7 SOME GENERALIZATIONS AND COMPLEMENTS 412 7.1
NONHOMOGENEOUS STATE EQUATION 412 7.2 TIME-DEPENDENT STATE EQUATION AND
COST FUNCTION . 414 7.3 DUAL RICCATI EQUATION 416 8 EXAMPLES OF
CONTROLLED SYSTEMS 418 8.1 PARABOLIC EQUATIONS 418 8.2 WAVE EQUATION 420
8.3 DELAY EQUATIONS 423 8.4 EVOLUTION EQUATIONS IN NONCYLINDRICAL
DOMAINS 428 CONTENTS XXV 2 UNBOUNDED CONTROL OPERATORS: PARABOLIC
EQUATIONS WITH CONTROL ON THE BOUNDARY 431 1 INTRODUCTION 431 2 RICCATI
EQUATION 438 2.1 NOTATION 438 2.2 RICCATI EQUATION FOR A 1/2 439 2.3
SOLUTION OF THE RICCATI EQUATION FOR A 1/2 446 3 DYNAMIC PROGRAMMING
454 3 UNBOUNDED CONTROL OPERATORS: HYPERBOLIC EQUATIONS WITH CONTROL ON
THE BOUNDARY 459 1 INTRODUCTION 459 2 RICCATI EQUATION 462 3 DYNAMIC
PROGRAMMING 463 4 EXAMPLES OF CONTROLLED HYPERBOLIC SYSTEMS 466 5 SOME
RESULT FOR GENERAL SEMIGROUPS 471 PART V QUADRATIC OPTIMAL CONTROL:
INFINITE TIME HORIZON 1 BOUNDED CONTROL OPERATORS: CONTROL INSIDE THE
DOMAIN . 479 1 INTRODUCTION AND SETTING OF THE PROBLEM 479 2 THE
ALGEBRAIC RICCATI EQUATION 480 3 SOLUTION OF THE CONTROL PROBLEM 486 3.1
FEEDBACK OPERATOR AND DETECTABILITY 487 3.2 STABILIZABILITY AND
STABILITY OF THE CLOSED LOOP OPERATOR F IN THE POINT SPECTRUM CASE 489
3.3 STABILIZABILITY 490 3.4 EXPONENTIAL STABILITY OF F 492 4 QUALITATIVE
PROPERTIES OF THE SOLUTIONS OF THE RICCATI EQUATION 493 4.1 LOCAL
STABILITY RESULTS 494 4.2 ATTRACTIVITY PROPERTIES OF A STATIONARY
SOLUTION 495 4.3 MAXIMAL SOLUTIONS 497 4.4 CONTINUOUS DEPENDENCE OF
STATIONARY SOLUTIONS WITH RESPECT TO THE DATA 501 4.5 PERIODIC SOLUTIONS
OF THE RICCATI EQUATION 502 5 SOME GENERALIZATIONS AND COMPLEMENTS 505
5.1 NONHOMOGENEOUS STATE EQUATION 505 5.2 TIME-DEPENDENT STATE EQUATION
AND COST FUNCTION . 507 5.3 PERIODIC CONTROL PROBLEMS 509 6 EXAMPLES
OF CONTROLLED SYSTEMS 513 6.1 PARABOLIC EQUATIONS 513 6.2 WAVE EQUATION
514 6.3 STRONGLY DAMPED WAVE EQUATION 515 XXVI CONTENTS 2 UNBOUNDED
CONTROL OPERATORS: PARABOLIC EQUATIONS WITH CONTROL ON THE BOUNDARY 517
1 INTRODUCTION AND SETTING OF THE PROBLEM 517 2 THE ALGEBRAIC RICCATI
EQUATION 518 3 DYNAMIC PROGRAMMING 521 3.1 EXISTENCE AND UNIQUENESS OF
THE OPTIMAL CONTROL 521 3.2 FEEDBACK OPERATOR AND DETECTABILITY 523 3.3
STABILIZABILITY AND STABILITY OF F IN THE POINT SPECTRUM CASE 525 3
UNBOUNDED CONTROL OPERATORS: HYPERBOLIC EQUATIONS WITH CONTROL ON THE
BOUNDARY 529 1 INTRODUCTION AND SETTING OF THE PROBLEM 529 2 MAIN
RESULTS 530 3 SOME RESULT FOR GENERAL SEMIGROUPS 534 A AN ISOMORPHISM
RESULT 537 REFERENCES 541 INDEX 569 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Bensoussan, Alain 1940- Da Prato, Giuseppe 1936-2023 Delfour, Michel C. 1943- Mitter, Sanjoy K. 1933- |
| author_GND | (DE-588)13295947X (DE-588)121352641 (DE-588)17252931X (DE-588)122995430 |
| author_facet | Bensoussan, Alain 1940- Da Prato, Giuseppe 1936-2023 Delfour, Michel C. 1943- Mitter, Sanjoy K. 1933- |
| author_role | aut aut aut aut |
| author_sort | Bensoussan, Alain 1940- |
| author_variant | a b ab p g d pg pgd m c d mc mcd s k m sk skm |
| building | Verbundindex |
| bvnumber | BV022198026 |
| callnumber-first | Q - Science |
| callnumber-label | QA402 |
| callnumber-raw | QA402.3 |
| callnumber-search | QA402.3 |
| callnumber-sort | QA 3402.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 880 |
| ctrlnum | (OCoLC)74650361 (DE-599)BVBBV022198026 |
| dewey-full | 629.8/312 |
| 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 | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| discipline_str_mv | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| edition | second edition |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04239nam a2200733 c 4500</leader><controlfield tag="001">BV022198026</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20211105 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">061219s2007 |||| |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">05,N44,0470</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">976672049</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">081764461X</subfield><subfield code="9">0-8176-4461-X</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780817644611</subfield><subfield code="9">978-0-8176-4461-1</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9780817644611</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">11424666</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)74650361</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV022198026</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA402.3</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">629.8/312</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 880</subfield><subfield code="0">(DE-625)143266:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">34G10</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">47D06</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">93C35</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">47N70</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">34H05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">93C95</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bensoussan, Alain</subfield><subfield code="d">1940-</subfield><subfield code="0">(DE-588)13295947X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Representation and control of infinite dimensional systems</subfield><subfield code="c">Bensoussan, Alain; Da Prato, Giuseppe; Delfour, Michel C.; Mitter, Sanjoy K.</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">second edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston ; Basel ; Berlin</subfield><subfield code="b">Birkhäuser</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xxvi, 575 Seiten</subfield><subfield code="b">Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Systems & control: foundations & applications</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">"The quadratic cost optimal control problem for systems described by linear ordinary differential equations occupies a central role in the study of control systems both from a theoretical and design point of view. The study of this problem over an infinite time horizon shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability, observability, stabilizability, and detectability. This theory is far more difficult for infinite dimensional systems such as those with time delays and distributed parameter systems. ... Part I reviews basic optimal control and game theory of finite dimensional systems, which serves as an introduction to the book. Part II deals with time evolution of some generic controlled infinite dimensional systems and contains a fairly complete account of semigroup theory. It incorporates interpolation theory and exhibits the role of semigroup theory in delay differential and partial differential equations. Part III studies the generic qualitative properties of controlled systems. Parts IV and V examine the optimal control of systems when performance is measured via a quadratic cost. Boundary control of parabolic and hyperbolic systems and exact controllability are also covered"--P. [4] of cover.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Commande, Théorie de la</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Optimisation mathématique</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Control theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical optimization</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Unendlichdimensionales System</subfield><subfield code="0">(DE-588)4207956-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kontrolltheorie</subfield><subfield code="0">(DE-588)4032317-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Optimale Kontrolle</subfield><subfield code="0">(DE-588)4121428-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lineare Differentialgleichung</subfield><subfield code="0">(DE-588)4206889-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Unendlichdimensionales System</subfield><subfield code="0">(DE-588)4207956-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Lineare Differentialgleichung</subfield><subfield code="0">(DE-588)4206889-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Optimale Kontrolle</subfield><subfield code="0">(DE-588)4121428-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Unendlichdimensionales System</subfield><subfield code="0">(DE-588)4207956-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Kontrolltheorie</subfield><subfield code="0">(DE-588)4032317-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Da Prato, Giuseppe</subfield><subfield code="d">1936-2023</subfield><subfield code="0">(DE-588)121352641</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Delfour, Michel C.</subfield><subfield code="d">1943-</subfield><subfield code="0">(DE-588)17252931X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Mitter, Sanjoy K.</subfield><subfield code="d">1933-</subfield><subfield code="0">(DE-588)122995430</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-0-8176-4581-6</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="q">text/html</subfield><subfield code="u">http://deposit.dnb.de/cgi-bin/dokserv?id=2687851&prov=M&dok_var=1&dok_ext=htm</subfield><subfield code="3">Inhaltstext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015409501&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-015409501</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV022198026 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:23:27Z |
| indexdate | 2024-07-09T20:52:11Z |
| institution | BVB |
| isbn | 081764461X 9780817644611 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015409501 |
| oclc_num | 74650361 |
| open_access_boolean | |
| owner | DE-703 DE-11 DE-29T DE-739 DE-83 |
| owner_facet | DE-703 DE-11 DE-29T DE-739 DE-83 |
| physical | xxvi, 575 Seiten Diagramme |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Systems & control: foundations & applications |
| spelling | Bensoussan, Alain 1940- (DE-588)13295947X aut Representation and control of infinite dimensional systems Bensoussan, Alain; Da Prato, Giuseppe; Delfour, Michel C.; Mitter, Sanjoy K. second edition Boston ; Basel ; Berlin Birkhäuser 2007 xxvi, 575 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Systems & control: foundations & applications "The quadratic cost optimal control problem for systems described by linear ordinary differential equations occupies a central role in the study of control systems both from a theoretical and design point of view. The study of this problem over an infinite time horizon shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability, observability, stabilizability, and detectability. This theory is far more difficult for infinite dimensional systems such as those with time delays and distributed parameter systems. ... Part I reviews basic optimal control and game theory of finite dimensional systems, which serves as an introduction to the book. Part II deals with time evolution of some generic controlled infinite dimensional systems and contains a fairly complete account of semigroup theory. It incorporates interpolation theory and exhibits the role of semigroup theory in delay differential and partial differential equations. Part III studies the generic qualitative properties of controlled systems. Parts IV and V examine the optimal control of systems when performance is measured via a quadratic cost. Boundary control of parabolic and hyperbolic systems and exact controllability are also covered"--P. [4] of cover. Commande, Théorie de la Optimisation mathématique Control theory Mathematical optimization Unendlichdimensionales System (DE-588)4207956-1 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Lineare Differentialgleichung (DE-588)4206889-7 gnd rswk-swf Unendlichdimensionales System (DE-588)4207956-1 s Lineare Differentialgleichung (DE-588)4206889-7 s Optimale Kontrolle (DE-588)4121428-6 s DE-604 Kontrolltheorie (DE-588)4032317-1 s 1\p DE-604 Da Prato, Giuseppe 1936-2023 (DE-588)121352641 aut Delfour, Michel C. 1943- (DE-588)17252931X aut Mitter, Sanjoy K. 1933- (DE-588)122995430 aut Erscheint auch als Online-Ausgabe 978-0-8176-4581-6 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2687851&prov=M&dok_var=1&dok_ext=htm Inhaltstext GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015409501&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bensoussan, Alain 1940- Da Prato, Giuseppe 1936-2023 Delfour, Michel C. 1943- Mitter, Sanjoy K. 1933- Representation and control of infinite dimensional systems Commande, Théorie de la Optimisation mathématique Control theory Mathematical optimization Unendlichdimensionales System (DE-588)4207956-1 gnd Kontrolltheorie (DE-588)4032317-1 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Lineare Differentialgleichung (DE-588)4206889-7 gnd |
| subject_GND | (DE-588)4207956-1 (DE-588)4032317-1 (DE-588)4121428-6 (DE-588)4206889-7 |
| title | Representation and control of infinite dimensional systems |
| title_auth | Representation and control of infinite dimensional systems |
| title_exact_search | Representation and control of infinite dimensional systems |
| title_exact_search_txtP | Representation and control of infinite dimensional systems |
| title_full | Representation and control of infinite dimensional systems Bensoussan, Alain; Da Prato, Giuseppe; Delfour, Michel C.; Mitter, Sanjoy K. |
| title_fullStr | Representation and control of infinite dimensional systems Bensoussan, Alain; Da Prato, Giuseppe; Delfour, Michel C.; Mitter, Sanjoy K. |
| title_full_unstemmed | Representation and control of infinite dimensional systems Bensoussan, Alain; Da Prato, Giuseppe; Delfour, Michel C.; Mitter, Sanjoy K. |
| title_short | Representation and control of infinite dimensional systems |
| title_sort | representation and control of infinite dimensional systems |
| topic | Commande, Théorie de la Optimisation mathématique Control theory Mathematical optimization Unendlichdimensionales System (DE-588)4207956-1 gnd Kontrolltheorie (DE-588)4032317-1 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Lineare Differentialgleichung (DE-588)4206889-7 gnd |
| topic_facet | Commande, Théorie de la Optimisation mathématique Control theory Mathematical optimization Unendlichdimensionales System Kontrolltheorie Optimale Kontrolle Lineare Differentialgleichung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2687851&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015409501&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bensoussanalain representationandcontrolofinfinitedimensionalsystems AT dapratogiuseppe representationandcontrolofinfinitedimensionalsystems AT delfourmichelc representationandcontrolofinfinitedimensionalsystems AT mittersanjoyk representationandcontrolofinfinitedimensionalsystems |