000 | 06445cam a2200625Ia 4500 | ||
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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 |
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019 |
_a171113690 _a441762603 _a647546658 _a779919906 |
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020 | _a9780444516329 | ||
020 | _a0444516328 | ||
020 | _a0080457347 (electronic bk.) | ||
020 | _a9780080457345 (electronic bk.) | ||
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_aNZ1 _b12434426 |
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_a(OCoLC)162130148 _z(OCoLC)171113690 _z(OCoLC)441762603 _z(OCoLC)647546658 _z(OCoLC)779919906 |
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037 |
_a108360:108405 _bElsevier Science & Technology _nhttp://www.sciencedirect.com |
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_aQA402.3 _b.F367 2005eb |
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_aQA _2lcco |
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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. |
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300 |
_a1 online resource (xii, 320 p.) : _bill. |
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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 |
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650 | 7 |
_aControl theory. _2fast _0(OCoLC)fst00877085 |
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650 | 7 |
_aLinear control systems. _2fast _0(OCoLC)fst00999065 |
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650 | 7 |
_aMathematical optimization. _2fast _0(OCoLC)fst01012099 |
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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 |
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938 |
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938 |
_aYBP Library Services _bYANK _n2585685 |
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938 |
_aIngram Digital eBook Collection _bIDEB _n63386 |
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942 | _cEB | ||
994 |
_aC0 _bTEF |
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999 |
_c21875 _d21875 |