000 06445cam a2200625Ia 4500
001 ocn162130148
003 OCoLC
005 20141103172226.0
006 m o d
007 cr cn|||||||||
008 070802s2005 ne a ob 001 0 eng d
040 _aOPELS
_beng
_cOPELS
_dOCLCG
_dOPELS
_dOCLCQ
_dMERUC
_dE7B
_dYDXCP
_dIDEBK
_dTULIB
_dOCLCO
_dOCLCQ
_dOPELS
_dOCLCF
_dDEBBG
019 _a171113690
_a441762603
_a647546658
_a779919906
020 _a9780444516329
020 _a0444516328
020 _a0080457347 (electronic bk.)
020 _a9780080457345 (electronic bk.)
029 1 _aNZ1
_b12434426
029 1 _aAU@
_b000048129900
029 1 _aDEBBG
_bBV036962230
035 _a(OCoLC)162130148
_z(OCoLC)171113690
_z(OCoLC)441762603
_z(OCoLC)647546658
_z(OCoLC)779919906
037 _a108360:108405
_bElsevier Science & Technology
_nhttp://www.sciencedirect.com
050 4 _aQA402.3
_b.F367 2005eb
072 7 _aQA
_2lcco
082 0 4 _a629.8
_222
049 _aTEFA
100 1 _aFattorini, H. O.
_q(Hector O.),
_d1938-
245 1 0 _aInfinite dimensional linear control systems
_h[electronic resource] :
_bthe time optimal and norm optimal problems /
_cH.O. Fattorini.
250 _a1st ed.
260 _aAmsterdam ;
_aBoston :
_bElsevier,
_c2005.
300 _a1 online resource (xii, 320 p.) :
_bill.
490 1 _aNorth-Holland mathematics studies,
_x0304-0208 ;
_v201
520 _aFor 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.
505 0 _aPREFACE -- 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.
504 _aIncludes bibliographical references (p. 309-318) and index.
588 _aDescription based on print version record.
650 0 _aControl theory.
650 0 _aCalculus of variations.
650 0 _aLinear control systems.
650 0 _aMathematical optimization.
650 7 _aCalculus of variations.
_2fast
_0(OCoLC)fst00844140
650 7 _aControl theory.
_2fast
_0(OCoLC)fst00877085
650 7 _aLinear control systems.
_2fast
_0(OCoLC)fst00999065
650 7 _aMathematical optimization.
_2fast
_0(OCoLC)fst01012099
655 4 _aElectronic books.
776 0 8 _iPrint version:
_aFattorini, H. O. (Hector O.), 1938-
_tInfinite dimensional linear control systems.
_b1st ed.
_dAmsterdam ; Boston : Elsevier, 2005
_z0444516328
_z9780444516329
_w(DLC) 2005049489
_w(OCoLC)60320153
830 0 _aNorth-Holland mathematics studies ;
_v201.
_x0304-0208
856 4 0 _3ScienceDirect
_uhttp://www.sciencedirect.com/science/book/9780444516329
856 4 _uhttp://www.sciencedirect.com/science/publication?issn=03040208&volume=201
_3Volltext
938 _aebrary
_bEBRY
_nebr10138377
938 _aYBP Library Services
_bYANK
_n2585685
938 _aIngram Digital eBook Collection
_bIDEB
_n63386
942 _cEB
994 _aC0
_bTEF
999 _c21875
_d21875