Stability and sensitivity analysis for optimal control problems with control state constraints:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Warszawa
Inst. of Mathematics
2001
|
| Series: | Dissertationes mathematicae
394 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 51 S. |
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Titel: Stability and sensitivity analysis for optimal control problems with control state constraints
Autor: Malanowski, Kazimierz
Jahr: 2001
CONTENTS
1. Introduction .
2. Problem formulation and constraint qualifications .
3. Optimality condition and coercivity.
4. Application of abstract theorems.
5. Stability analysis for the accessory problem.
6. Differentiability of solutions to accessory problems
7. Lipschitz stability of solutions to nonlinear problems
8. Differentiability of solutions to nonlinear problems
9. Necessary conditions of stability and sensitivity . .
10. Conclusion .
References.
2000 Mathematics Subject Classification: 49K40, 49K15, 49K30.
Key words and phrases: parametric optimal control, nonlinear ordinary differential equations,
control-state constraints, Lipschitz continuity and differentiability of solutions.
Received 6.7.2000; revised version 20.10.2000.
Supported by the Polish State Committee for Scientific Research (KBN) grant 8 TllA 028 14.
Abstract
A family of parameter dependent optimal control problems (0)/t with smooth data for nonlinear
ODEs is considered. The problems are subject to pointwise mixed control-state constraints. It is
assumed that, for a reference value ho of the parameter, a solution of (0)/lQ exists. It is shown
that if
(i) independence, controllability and coercivity conditions are satisfied at the reference solu-
tion,
then
(ii) for each h from a neighborhood of ho, a locally unique solution to (0)/t and the associated
Lagrange multiplier exist, are Lipschitz continuous and Bouligand diflerentiable functions
of the parameter.
E, in addition, the dependence of the data on the parameter is strong, then (ii) implies (i).
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| publishDate | 2001 |
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| series | Dissertationes mathematicae |
| series2 | Dissertationes mathematicae |
| spelling | Malanowski, Kazimierz Verfasser aut Stability and sensitivity analysis for optimal control problems with control state constraints Kazimierz Malanowski Warszawa Inst. of Mathematics 2001 51 S. txt rdacontent n rdamedia nc rdacarrier Dissertationes mathematicae 394 Dissertationes mathematicae 394 (DE-604)BV000003039 394 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009524072&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Malanowski, Kazimierz Stability and sensitivity analysis for optimal control problems with control state constraints Dissertationes mathematicae |
| title | Stability and sensitivity analysis for optimal control problems with control state constraints |
| title_auth | Stability and sensitivity analysis for optimal control problems with control state constraints |
| title_exact_search | Stability and sensitivity analysis for optimal control problems with control state constraints |
| title_full | Stability and sensitivity analysis for optimal control problems with control state constraints Kazimierz Malanowski |
| title_fullStr | Stability and sensitivity analysis for optimal control problems with control state constraints Kazimierz Malanowski |
| title_full_unstemmed | Stability and sensitivity analysis for optimal control problems with control state constraints Kazimierz Malanowski |
| title_short | Stability and sensitivity analysis for optimal control problems with control state constraints |
| title_sort | stability and sensitivity analysis for optimal control problems with control state constraints |
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