A numerical method for approximating the solution of fuzzy fractional optimal control problems in caputo sense using legendre functions

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dc.authoridTofigh Allahviranloo / 0000-0002-6673-3560en_US
dc.authorscopusidTofigh Allahviranloo / 8834494700
dc.authorwosidTofigh Allahviranloo / V-4843-2019en_US
dc.contributor.authorMirvakili, Massoud
dc.contributor.authorAllahviranloo, Tofigh
dc.contributor.authorSoltanian, Fahimeh
dc.date.accessioned2022-08-08T11:28:21Z
dc.date.available2022-08-08T11:28:21Z
dc.date.issued2022en_US
dc.departmentİstinye Üniversitesi, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractFractional order differential equations accurately model dynamic systems and processes. In some of the fractional optimal control problems (FOCPs), due to the ambiguity in the initial conditions and the transfer of ambiguity to the solution, it is necessary to use fuzzy mathematics. In this paper, a numerical method is presented to approximate the solution for a class of Fuzzy Fractional Optimal Control Problems (FFOCPs) using the Legendre basis functions. The fuzzy fractional derivative is described in the Caputo sense. The performance index of an FFOCP is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a set of Fuzzy Fractional Differential Equations (FFDEs). After obtaining Euler-Lagrange equations for FFOCPs and the necessary and sufficient conditions for the existence of solutions, using the definition of generalized Hukuhara differentiability (types I, II), the problem is considered in two cases. Then the distance function and an approach similar to the variational type along with the Lagrange multiplier method are used to formulate and solve the equations in a system. Time-invariant and time-varying examples are provided to assess the presented method. Numerical results show a similar trend for the state and control variables for various numbers of Legendre polynomials. Also, the convergence of state and control variables for the time-invariant system can be seen, and the same is true for control variables for the time-varying system.en_US
dc.identifier.citationMirvakili, M., Allahviranloo, T., Soltanian, F. (2022). A numerical method for approximating the solution of fuzzy fractional optimal control problems in caputo sense using legendre functions. Journal of Intelligent & Fuzzy System, 43(4), 3827-3858.en_US
dc.identifier.doi10.3233/JIFS-210583en_US
dc.identifier.endpage3858en_US
dc.identifier.issn1064-1246en_US
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-85134883597en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage3827en_US
dc.identifier.urihttps://doi.org/10.3233/JIFS-210583
dc.identifier.urihttps://hdl.handle.net/20.500.12713/3072
dc.identifier.volume43en_US
dc.identifier.wosWOS:000831233800106en_US
dc.identifier.wosqualityQ4en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.institutionauthorAllahviranloo, Tofigh
dc.language.isoenen_US
dc.publisherIOS PRESSen_US
dc.relation.ispartofJOURNAL OF INTELLIGENT & FUZZY SYSTEMSen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectFuzzy Fractional Optimal Control Problemen_US
dc.subjectCaputo Derivativeen_US
dc.subjectLegendre Basis Functionen_US
dc.subjectEuler-Lagrange Equationsen_US
dc.subjectGeneralized Hukuhara Differentiabilityen_US
dc.subjectNumerical Methoden_US
dc.titleA numerical method for approximating the solution of fuzzy fractional optimal control problems in caputo sense using legendre functionsen_US
dc.typeArticleen_US

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