Local controllability and optimal control for\newline a model of combined anticancer therapy with control delays
We study some control properties of a class of two-compartmental models of response to anticancer treatment which combines anti-angiogenic and cytotoxic drugs and take into account multiple control delays. We formulate sufficient local controllability conditions for semilinear systems resulting from...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017013 |
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| _version_ | 1832590089992011776 |
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| author | Jerzy Klamka Helmut Maurer Andrzej Swierniak |
| author_facet | Jerzy Klamka Helmut Maurer Andrzej Swierniak |
| author_sort | Jerzy Klamka |
| collection | DOAJ |
| description | We study some control properties of a class of two-compartmental models of response to anticancer treatment which combines anti-angiogenic and cytotoxic drugs and take into account multiple control delays. We formulate sufficient local controllability conditions for semilinear systems resulting from these models. The control delays are related to PK/PD effects and some clinical recommendations, e.g., normalization of the vascular network. The optimized protocols of the combined therapy for the model, considered as solutions to an optimal control problem with delays in control, are found using necessary conditions of optimality and numerical computations. Our numerical approach uses dicretization and nonlinear programming methods as well as the direct optimization of switching times. The structural sensitivity of the considered control properties and optimal solutions is also discussed. |
| format | Article |
| id | doaj-art-f38f0ee5cee348d4b29d96542ed31644 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-f38f0ee5cee348d4b29d96542ed316442025-01-24T02:39:32ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-01-0114119521610.3934/mbe.2017013Local controllability and optimal control for\newline a model of combined anticancer therapy with control delaysJerzy Klamka0Helmut Maurer1Andrzej Swierniak2Silesian University of Technology, Department of Automatic Control, Akademicka 16, 44101 Gliwice, PolandUniversity of Münster, Institute of Computational and Applied Mathematics, Einsteinstr. 62,48149 Münster, GermanySilesian University of Technology, Department of Automatic Control, Akademicka 16, 44101 Gliwice, PolandWe study some control properties of a class of two-compartmental models of response to anticancer treatment which combines anti-angiogenic and cytotoxic drugs and take into account multiple control delays. We formulate sufficient local controllability conditions for semilinear systems resulting from these models. The control delays are related to PK/PD effects and some clinical recommendations, e.g., normalization of the vascular network. The optimized protocols of the combined therapy for the model, considered as solutions to an optimal control problem with delays in control, are found using necessary conditions of optimality and numerical computations. Our numerical approach uses dicretization and nonlinear programming methods as well as the direct optimization of switching times. The structural sensitivity of the considered control properties and optimal solutions is also discussed.https://www.aimspress.com/article/doi/10.3934/mbe.2017013combined cancer therapylocal controllabilityoptimal controlcontrol delays |
| spellingShingle | Jerzy Klamka Helmut Maurer Andrzej Swierniak Local controllability and optimal control for\newline a model of combined anticancer therapy with control delays Mathematical Biosciences and Engineering combined cancer therapy local controllability optimal control control delays |
| title | Local controllability and optimal control for\newline a model of combined anticancer therapy with control delays |
| title_full | Local controllability and optimal control for\newline a model of combined anticancer therapy with control delays |
| title_fullStr | Local controllability and optimal control for\newline a model of combined anticancer therapy with control delays |
| title_full_unstemmed | Local controllability and optimal control for\newline a model of combined anticancer therapy with control delays |
| title_short | Local controllability and optimal control for\newline a model of combined anticancer therapy with control delays |
| title_sort | local controllability and optimal control for newline a model of combined anticancer therapy with control delays |
| topic | combined cancer therapy local controllability optimal control control delays |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017013 |
| work_keys_str_mv | AT jerzyklamka localcontrollabilityandoptimalcontrolfornewlineamodelofcombinedanticancertherapywithcontroldelays AT helmutmaurer localcontrollabilityandoptimalcontrolfornewlineamodelofcombinedanticancertherapywithcontroldelays AT andrzejswierniak localcontrollabilityandoptimalcontrolfornewlineamodelofcombinedanticancertherapywithcontroldelays |