Title:
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On the existence of optimal controls for nonlinear infinite dimensional systems (English) |
Author:
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Fiacca, Antonella |
Author:
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Papageorgiou, Nikolaos S. |
Author:
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Papalini, Francesca |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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48 |
Issue:
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2 |
Year:
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1998 |
Pages:
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291-312 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations. (English) |
Keyword:
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evolution triple |
Keyword:
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optimal control |
Keyword:
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monotone operator |
Keyword:
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hemicontinuous operator |
Keyword:
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parabolic system |
Keyword:
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property $(Q)$ |
MSC:
|
34G20 |
MSC:
|
34H05 |
MSC:
|
47N20 |
MSC:
|
49J25 |
MSC:
|
49J27 |
idZBL:
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Zbl 0955.34049 |
idMR:
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MR1624323 |
. |
Date available:
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2009-09-24T10:13:29Z |
Last updated:
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2020-07-03 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/127417 |
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Reference:
|
[1] N. U. Ahmed – K. L. Teo: Optimal Control of Distributed Parameter Systems.North Holland, New York, 1981. MR 0624064 |
Reference:
|
[2] E. Balder: Necessary and sufficient conditions for $L_1$-strong-weak lower semicontinuity of integral functionals.Nonlinear Analysis 11 (1987), 1399–1404. MR 0917861, 10.1016/0362-546X(87)90092-7 |
Reference:
|
[3] V. Barbu: Nonlinear Semigroups and Differential Equations in Banach Spaces.Noordhoff, Leyden, 1976. Zbl 0328.47035, MR 0390843 |
Reference:
|
[4] L. D. Berkovitz: Optimal Control Theory.Springer-Verlag, New York, 1974. Zbl 0295.49001, MR 0372707 |
Reference:
|
[5] L. Cesari: Existence theorems for weak and usual optimal solutions in Lagrange problems with unilateral constraints - I.Trans. Amer. Math. Society 124 (1966), 369–412. Zbl 0145.12501, MR 0203542, 10.1090/S0002-9947-1966-0203542-1 |
Reference:
|
[6] L. Cesari: Optimization-Theory and Applications.Springer-Verlag, New York, 1983. Zbl 0506.49001, MR 0688142 |
Reference:
|
[7] G. A. Edgar: Measurability in a Banach space - II.Indiana J. Math. 28 (1979), 559–579. Zbl 0418.46034, MR 0542944, 10.1512/iumj.1979.28.28039 |
Reference:
|
[8] A. Fryszkowski: The generalization of Cellina’s Fixed Point Theorem.Studia Math. 78 (1983), 213–215. MR 0766717, 10.4064/sm-78-2-213-215 |
Reference:
|
[9] S. H. Hou: On Property $(Q)$ and other semicontinuity properties of multifunctions.Pacific Journal Math. 103 (1982), 39–56. MR 0687963, 10.2140/pjm.1982.103.39 |
Reference:
|
[10] V. Levin: Borel sections of many valued maps.Siberian Math. J. 19 (1979), 434–438. Zbl 0409.54048, 10.1007/BF01875294 |
Reference:
|
[11] J. L. Lions: Optimal Control of Systems Governed by Partial Differential Equations.Springer, Berlin, 1971. Zbl 0203.09001, MR 0271512 |
Reference:
|
[12] N. S. Papageorgiou: On measurable multifunctions with applications to random multivalued equations.Math. Japonica 32 (1987), 437–464. Zbl 0634.28005, MR 0914749 |
Reference:
|
[13] N. S. Papageorgiou: Convergence theorems for Banach space-valued integrable multifunctions.Intern. J. Math. and Math. Sci. 10 (1987), 433–442. Zbl 0619.28009, MR 0896595, 10.1155/S0161171287000516 |
Reference:
|
[14] D. Wagner: Survey on measurable selection theorems.SIAM J. Control Optim. 15 (1977), 859–903. MR 0486391, 10.1137/0315056 |
Reference:
|
[15] E. Zeidler: Nonlinear Functional Analysis and Its Application II.Springer, New York, 1990. MR 0816732 |
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