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Sensitivity analysis for optimal control problems governed by nonlinear evolution inclusions
ID
Papageorgiou, Nikolaos S.
(
Author
),
ID
Rǎdulescu, Vicenţiu
(
Author
),
ID
Repovš, Dušan
(
Author
)
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Abstract
We consider a nonlinear optimal control problem governed by a nonlinear evolution inclusion and depending on a parameter ▫$\lambda$▫. First we examine the dynamics of the problem and establish the nonemptiness of the solution set and produce continuous selections of the solution multifunction ▫$\xi \mapsto S(\xi)$▫ (▫$\xi$▫ being the initial condition). These results are proved in a very general framework and are of independent interest as results about evolution inclusions. Then we use them to study the sensitivity properties of the optimal control problem. We show that we have Hadamard well-posedness (continuity of the value function), and we establish the continuity properties of the optimal multifunction. Finally, we present an application on a nonlinear parabolic distributed parameter system.
Language:
English
Keywords:
evolution triple
,
evolution inclusion
,
PG and G convergence
,
compact embedding
,
Hadamard well-posedness
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
PEF - Faculty of Education
FMF - Faculty of Mathematics and Physics
Year:
2017
Number of pages:
Str. 199-235
Numbering:
Vol. 6, iss. 2
PID:
20.500.12556/RUL-110027
UDC:
517.951/.952
ISSN on article:
2191-9496
DOI:
10.1515/anona-2016-0096
COBISS.SI-ID:
17696089
Publication date in RUL:
11.09.2019
Views:
792
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451
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Record is a part of a journal
Title:
Advances in nonlinear analysis
Publisher:
De Gruyter
ISSN:
2191-9496
COBISS.SI-ID:
16253785
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