Equivalent Formulations of Optimal Control Problems with Maximum Cost and Applications
Abstract We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential incl...
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| Autor*in: |
Molina, Emilio [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: Journal of optimization theory and applications - Springer US, 1967, 195(2022), 3 vom: 29. Sept., Seite 953-975 |
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| Übergeordnetes Werk: |
volume:195 ; year:2022 ; number:3 ; day:29 ; month:09 ; pages:953-975 |
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| DOI / URN: |
10.1007/s10957-022-02094-z |
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| 520 | |a Abstract We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state constraint. For the latter we also propose a scheme that approximates from below the optimal value. These approaches are illustrated and discussed in several examples. | ||
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| 650 | 4 | |a Mayer problem | |
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| 650 | 4 | |a Differential inclusion | |
| 650 | 4 | |a Numerical schemes | |
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10.1007/s10957-022-02094-z doi (DE-627)OLC2079983180 (DE-He213)s10957-022-02094-z-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Molina, Emilio verfasserin aut Equivalent Formulations of Optimal Control Problems with Maximum Cost and Applications 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state constraint. For the latter we also propose a scheme that approximates from below the optimal value. These approaches are illustrated and discussed in several examples. Optimal control Maximum cost Mayer problem State constraint Differential inclusion Numerical schemes SIR model Rapaport, Alain (orcid)0000-0002-8515-0838 aut Ramírez, Héctor (orcid)0000-0002-6239-1890 aut Enthalten in Journal of optimization theory and applications Springer US, 1967 195(2022), 3 vom: 29. Sept., Seite 953-975 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:195 year:2022 number:3 day:29 month:09 pages:953-975 https://doi.org/10.1007/s10957-022-02094-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 SA 6420 SA 6420 AR 195 2022 3 29 09 953-975 |
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10.1007/s10957-022-02094-z doi (DE-627)OLC2079983180 (DE-He213)s10957-022-02094-z-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Molina, Emilio verfasserin aut Equivalent Formulations of Optimal Control Problems with Maximum Cost and Applications 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state constraint. For the latter we also propose a scheme that approximates from below the optimal value. These approaches are illustrated and discussed in several examples. Optimal control Maximum cost Mayer problem State constraint Differential inclusion Numerical schemes SIR model Rapaport, Alain (orcid)0000-0002-8515-0838 aut Ramírez, Héctor (orcid)0000-0002-6239-1890 aut Enthalten in Journal of optimization theory and applications Springer US, 1967 195(2022), 3 vom: 29. Sept., Seite 953-975 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:195 year:2022 number:3 day:29 month:09 pages:953-975 https://doi.org/10.1007/s10957-022-02094-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 SA 6420 SA 6420 AR 195 2022 3 29 09 953-975 |
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10.1007/s10957-022-02094-z doi (DE-627)OLC2079983180 (DE-He213)s10957-022-02094-z-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Molina, Emilio verfasserin aut Equivalent Formulations of Optimal Control Problems with Maximum Cost and Applications 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state constraint. For the latter we also propose a scheme that approximates from below the optimal value. These approaches are illustrated and discussed in several examples. Optimal control Maximum cost Mayer problem State constraint Differential inclusion Numerical schemes SIR model Rapaport, Alain (orcid)0000-0002-8515-0838 aut Ramírez, Héctor (orcid)0000-0002-6239-1890 aut Enthalten in Journal of optimization theory and applications Springer US, 1967 195(2022), 3 vom: 29. Sept., Seite 953-975 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:195 year:2022 number:3 day:29 month:09 pages:953-975 https://doi.org/10.1007/s10957-022-02094-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 SA 6420 SA 6420 AR 195 2022 3 29 09 953-975 |
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10.1007/s10957-022-02094-z doi (DE-627)OLC2079983180 (DE-He213)s10957-022-02094-z-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Molina, Emilio verfasserin aut Equivalent Formulations of Optimal Control Problems with Maximum Cost and Applications 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state constraint. For the latter we also propose a scheme that approximates from below the optimal value. These approaches are illustrated and discussed in several examples. Optimal control Maximum cost Mayer problem State constraint Differential inclusion Numerical schemes SIR model Rapaport, Alain (orcid)0000-0002-8515-0838 aut Ramírez, Héctor (orcid)0000-0002-6239-1890 aut Enthalten in Journal of optimization theory and applications Springer US, 1967 195(2022), 3 vom: 29. Sept., Seite 953-975 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:195 year:2022 number:3 day:29 month:09 pages:953-975 https://doi.org/10.1007/s10957-022-02094-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 SA 6420 SA 6420 AR 195 2022 3 29 09 953-975 |
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10.1007/s10957-022-02094-z doi (DE-627)OLC2079983180 (DE-He213)s10957-022-02094-z-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Molina, Emilio verfasserin aut Equivalent Formulations of Optimal Control Problems with Maximum Cost and Applications 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state constraint. For the latter we also propose a scheme that approximates from below the optimal value. These approaches are illustrated and discussed in several examples. Optimal control Maximum cost Mayer problem State constraint Differential inclusion Numerical schemes SIR model Rapaport, Alain (orcid)0000-0002-8515-0838 aut Ramírez, Héctor (orcid)0000-0002-6239-1890 aut Enthalten in Journal of optimization theory and applications Springer US, 1967 195(2022), 3 vom: 29. Sept., Seite 953-975 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:195 year:2022 number:3 day:29 month:09 pages:953-975 https://doi.org/10.1007/s10957-022-02094-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 SA 6420 SA 6420 AR 195 2022 3 29 09 953-975 |
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Equivalent Formulations of Optimal Control Problems with Maximum Cost and Applications |
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Abstract We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state constraint. For the latter we also propose a scheme that approximates from below the optimal value. These approaches are illustrated and discussed in several examples. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state constraint. For the latter we also propose a scheme that approximates from below the optimal value. These approaches are illustrated and discussed in several examples. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state constraint. For the latter we also propose a scheme that approximates from below the optimal value. These approaches are illustrated and discussed in several examples. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| title_short |
Equivalent Formulations of Optimal Control Problems with Maximum Cost and Applications |
| url |
https://doi.org/10.1007/s10957-022-02094-z |
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| author2 |
Rapaport, Alain Ramírez, Héctor |
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Rapaport, Alain Ramírez, Héctor |
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| doi_str |
10.1007/s10957-022-02094-z |
| up_date |
2024-07-04T02:36:06.163Z |
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7.3991537 |