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An optimization technique for solving a class of nonlinear fractional optimal control problems: Application in cancer treatment

2021Journal article Embargoed access
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dc.contributor.authorHassani, H.
dc.contributor.authorMachado, J. A. Tenreiro
dc.contributor.authorMehrabi, S.
dc.date.accessioned2021-09-28T14:50:05Z
dc.date.embargo2031-12
dc.date.issued2021
dc.description.abstractThis paper proposes an optimization method for solving a general form of nonlinear fractional optimal control problems (NFOCP) governed by nonlinear fractional dynamical systems and mixed conditions. A model for cancer treatment based on the NFOCP is developed, by including the population of immune cells, tumor cells, normal cells, fat cells, chemotherapeutic and immunotherapeutic drug concentrations. The aim behind the NFOCP is to find the optimal doses of chemotherapeutic and immunotherapeutic drugs which minimize the difference between the numbers of tumor and normal cells. The proposed approach includes inserting weight constants for the tumor and normal cells in the cost functional so that the normal cell population is large minimizing, therefore, the tumor burden. The method approximates the solutions of the NFOCP using the generalized shifted Legendre polynomials (GSLP). Operational matrices of integer and fractional derivatives are derived for the GSLP. The Gaussian quadrature rule and the Lagrange multipliers method reduce the NFOCP to a system of algebraic equations. Additionally, the error analysis of the algorithm is considered. Numerical examples demonstrate the effectiveness of the method.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.doi10.1016/j.apm.2021.01.004pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.22/18607
dc.language.isoengpt_PT
dc.publisherElsevierpt_PT
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S0307904X2100010Xpt_PT
dc.subjectGeneralized shifted Legendre polynomialspt_PT
dc.subjectNonlinear fractional optimal control problemspt_PT
dc.subjectGaussian quadrature rulept_PT
dc.subjectOperational matrixpt_PT
dc.subjectOptimization methodpt_PT
dc.subjectCancer treatmentpt_PT
dc.titleAn optimization technique for solving a class of nonlinear fractional optimal control problems: Application in cancer treatmentpt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage884pt_PT
oaire.citation.startPage868pt_PT
oaire.citation.titleApplied Mathematical Modellingpt_PT
oaire.citation.volume93pt_PT
person.familyNameTenreiro Machado
person.givenNameJ. A.
person.identifier.ciencia-id7A18-4935-5B29
person.identifier.orcid0000-0003-4274-4879
person.identifier.ridM-2173-2013
person.identifier.scopus-author-id55989030100
rcaap.rightsembargoedAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication82cd5c17-07b6-492b-b3e3-ecebdad1254f
relation.isAuthorOfPublication.latestForDiscovery82cd5c17-07b6-492b-b3e3-ecebdad1254f

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