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Infinite dimensional linear control ...

Fattorini, H. O. (1938-)

Infinite dimensional linear control systemsthe time optimal and norm optimal problems /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Infinite dimensional linear control systemsH.O. Fattorini.
Reminder of title:	the time optimal and norm optimal problems /
Author:	Fattorini, H. O.
Published:	Amsterdam ;Elsevier,2005.
Description:	xii, 320 p. :ill. ;25 cm.
Series:	North-Holland mathematics studies,
Subject:	Control theory.
Online resource:	An electronic book accessible through the World Wide Web; click for information
Online resource:	http://www.engineeringvillage.com/controller/servlet/OpenURL?genre=book&isbn=9780444516329
Online resource:	http://www.loc.gov/catdir/enhancements/fy0726/2005049489-d.html
Online resource:	http://www.loc.gov/catdir/enhancements/fy0625/2005049489-t.html
ISBN:	9780444516329

Infinite dimensional linear control systemsthe time optimal and norm optimal problems /
Fattorini, H. O.1938-

Infinite dimensional linear control systemsthe time optimal and norm optimal problems /[electronic resource] :H.O. Fattorini. - 1st ed. - Amsterdam ;Elsevier,2005. - xii, 320 p. :ill. ;25 cm. - North-Holland mathematics studies,2010304-0208 ;.

Includes bibliographical references (p. 309-318) and index.

PREFACE -- CHAPTER 1: INTRODUCTIONP> -- 1.1 Finite dimensional systems: the maximum principle. -- 1.2. Finite dimensional systems: existence and uniqueness. -- 1.3. Infinite dimensional systems. -- CHAPTER 2: SYSTEMS WITH STRONGLY MEASURABLE CONTROLS, I -- 2.1. The reachable space and the bang-bang property -- 2.2. Reversible systems -- 2.3. The reachable space and its dual, I -- 2.4. The reachable space and its dual, II -- 2.5. The maximum principle -- 2.6. Vanishing of the costate and nonuniqueness for norm optimal controls -- 2.7. Vanishing of the costate for time optimal controls -- 2.8. Singular norm optimal controls -- 2.9. Singular norm optimal controls and singular functionals -- CHAPTER 3: SYSTEMS WITH STRONGLY MEASURABLE CONTROLS, II -- 3.1. Existence and uniqueness of optimal controls -- 3.2. The weak maximum principle and the time optimal problem -- 3.3. Modeling of parabolic equations -- 3.4. Weakly singular extremals -- 3.5. More on the weak maximum principle -- 3.6. Convergence of minimizing sequences and stability of optimal controls -- CHAPTER 4: OPTIMAL CONTROL OF HEAT PROPAGATION -- 4.1. Modeling of parabolic equations -- 4.2. Adjoints -- 4.3. Adjoint semigroups -- 4.4. The reachable space -- 4.5. The reachable space and its dual, I -- 4.6. The reachable space and its dual, II -- 4.7. The maximum principle -- 4.8. Existence, uniqueness and stability of optimal controls -- 4.9. Examples and applications -- CHAPTER 5: OPTIMAL CONTROL OF DIFFUSIONS -- 5.1. Modeling of parabolic equations -- 5.2. Dual spaces -- 5.3. The reachable space and its dual -- 5.4. The maximum principle -- 5.5. Existence of optimal controls; uniqueness and stability of supports -- 5.6. Examples and applications. -- CHAPTER 6: APPENDIX -- 6.1 Self adjoint operators, I -- 6.2 Self adjoint operators, II -- 6.3 Related research -- REFERENCES -- NOTATION AND SUBJECT INDEX.

For more than forty years, the equation y(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until recently, and some have never been solved. This book is a survey of all results know to the author, with emphasis on very recent results (1999 to date). The book is restricted to linear equations and two particular problems (the time optimal problem, the norm optimal problem) which results in a more focused and concrete treatment. As experience shows, results on linear equations are the basis for the treatment of their semilinear counterparts, and techniques for the time and norm optimal problems can often be generalized to more general cost functionals. The main object of this book is to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y(t) = Ay(t) + u(t) that ends at the very latest frontier of research, with open problems and indications for future research. Key features: Applications to optimal diffusion processes. Applications to optimal heat propagation processes. Modelling of optimal processes governed by partial differential equations. Complete bibliography. Includes the latest research on the subject. Does not assume anything from the reader except basic functional analysis. Accessible to researchers and advanced graduate students alike Applications to optimal diffusion processes. Applications to optimal heat propagation processes. Modelling of optimal processes governed by partial differential equations. Complete bibliography. Includes the latest research on the subject. Does not assume anything from the reader except basic functional analysis. Accessible to researchers and advanced graduate students alike.

Electronic reproduction.
Amsterdam :
Elsevier Science & Technology,
2007.

Mode of access: World Wide Web.

ISBN: 9780444516329

Source: 108360:108405Elsevier Science & Technologyhttp://www.sciencedirect.comSubjects--Topical Terms:

182248
Control theory.
Index Terms--Genre/Form:

214472
Electronic books.

LC Class. No.: QA402.3 / .F367 2005eb

Dewey Class. No.: 629.8

Infinite dimensional linear control systemsthe time optimal and norm optimal problems /
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037 $a 108360:108405 $b Elsevier Science & Technology $n http://www.sciencedirect.com
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100 1 $a Fattorini, H. O. $q (Hector O.), $d 1938- $3 454769
245 1 0 $a Infinite dimensional linear control systems $h [electronic resource] : $b the time optimal and norm optimal problems / $c H.O. Fattorini.
250 $a 1st ed.
260 $a Amsterdam ; $a Boston : $b Elsevier, $c 2005.
300 $a xii, 320 p. : $b ill. ; $c 25 cm.
440 0 $a North-Holland mathematics studies, $x 0304-0208 ; $v 201
504 $a Includes bibliographical references (p. 309-318) and index.
505 0 $a PREFACE -- CHAPTER 1: INTRODUCTIONP> -- 1.1 Finite dimensional systems: the maximum principle. -- 1.2. Finite dimensional systems: existence and uniqueness. -- 1.3. Infinite dimensional systems. -- CHAPTER 2: SYSTEMS WITH STRONGLY MEASURABLE CONTROLS, I -- 2.1. The reachable space and the bang-bang property -- 2.2. Reversible systems -- 2.3. The reachable space and its dual, I -- 2.4. The reachable space and its dual, II -- 2.5. The maximum principle -- 2.6. Vanishing of the costate and nonuniqueness for norm optimal controls -- 2.7. Vanishing of the costate for time optimal controls -- 2.8. Singular norm optimal controls -- 2.9. Singular norm optimal controls and singular functionals -- CHAPTER 3: SYSTEMS WITH STRONGLY MEASURABLE CONTROLS, II -- 3.1. Existence and uniqueness of optimal controls -- 3.2. The weak maximum principle and the time optimal problem -- 3.3. Modeling of parabolic equations -- 3.4. Weakly singular extremals -- 3.5. More on the weak maximum principle -- 3.6. Convergence of minimizing sequences and stability of optimal controls -- CHAPTER 4: OPTIMAL CONTROL OF HEAT PROPAGATION -- 4.1. Modeling of parabolic equations -- 4.2. Adjoints -- 4.3. Adjoint semigroups -- 4.4. The reachable space -- 4.5. The reachable space and its dual, I -- 4.6. The reachable space and its dual, II -- 4.7. The maximum principle -- 4.8. Existence, uniqueness and stability of optimal controls -- 4.9. Examples and applications -- CHAPTER 5: OPTIMAL CONTROL OF DIFFUSIONS -- 5.1. Modeling of parabolic equations -- 5.2. Dual spaces -- 5.3. The reachable space and its dual -- 5.4. The maximum principle -- 5.5. Existence of optimal controls; uniqueness and stability of supports -- 5.6. Examples and applications. -- CHAPTER 6: APPENDIX -- 6.1 Self adjoint operators, I -- 6.2 Self adjoint operators, II -- 6.3 Related research -- REFERENCES -- NOTATION AND SUBJECT INDEX.
520 $a For more than forty years, the equation y(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until recently, and some have never been solved. This book is a survey of all results know to the author, with emphasis on very recent results (1999 to date). The book is restricted to linear equations and two particular problems (the time optimal problem, the norm optimal problem) which results in a more focused and concrete treatment. As experience shows, results on linear equations are the basis for the treatment of their semilinear counterparts, and techniques for the time and norm optimal problems can often be generalized to more general cost functionals. The main object of this book is to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y(t) = Ay(t) + u(t) that ends at the very latest frontier of research, with open problems and indications for future research. Key features: Applications to optimal diffusion processes. Applications to optimal heat propagation processes. Modelling of optimal processes governed by partial differential equations. Complete bibliography. Includes the latest research on the subject. Does not assume anything from the reader except basic functional analysis. Accessible to researchers and advanced graduate students alike Applications to optimal diffusion processes. Applications to optimal heat propagation processes. Modelling of optimal processes governed by partial differential equations. Complete bibliography. Includes the latest research on the subject. Does not assume anything from the reader except basic functional analysis. Accessible to researchers and advanced graduate students alike.
533 $a Electronic reproduction. $b Amsterdam : $c Elsevier Science & Technology, $d 2007. $n Mode of access: World Wide Web. $n System requirements: Web browser. $n Title from title screen (viewed on July 25, 2007). $n Access may be restricted to users at subscribing institutions.
650 0 $a Control theory. $3 182248
650 0 $a Calculus of variations. $3 191127
650 0 $a Linear control systems. $3 237159
650 0 $a Mathematical optimization. $3 183292
655 7 $a Electronic books. $2 local. $3 214472
710 2 $a ScienceDirect (Online service) $3 307425
776 1 $c Original $z 0444516328 $z 9780444516329 $w (DLC) 2005049489 $w (OCoLC)60320153
856 4 0 $3 ScienceDirect $u http://www.sciencedirect.com/science/publication?issn=03040208&volume=201 $z An electronic book accessible through the World Wide Web; click for information
856 4 0 $3 Referex $u http://www.engineeringvillage.com/controller/servlet/OpenURL?genre=book&isbn=9780444516329 $z An electronic book accessible through the World Wide Web; click for information
856 4 2 $3 Publisher description $u http://www.loc.gov/catdir/enhancements/fy0726/2005049489-d.html
856 4 1 $3 Table of contents only $u http://www.loc.gov/catdir/enhancements/fy0625/2005049489-t.html
994 $a C0 $b TEF

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