On the solution of fuzzy fractional optimal control problems with the Caputo derivative
This paper presents an extension to fractional optimal control problems with ambiguity. As the ambiguity is modeled with fuzzy method, we encounter with a fuzzy fractional optimal control problem. The objective in fuzzy fractional optimal control problem is to determine the best possible fuzzy contr...
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| Published in | Information sciences Vol. 421; pp. 218 - 236 |
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| Abstract | This paper presents an extension to fractional optimal control problems with ambiguity. As the ambiguity is modeled with fuzzy method, we encounter with a fuzzy fractional optimal control problem. The objective in fuzzy fractional optimal control problem is to determine the best possible fuzzy control which satisfies the related fuzzy fractional dynamic systems and minimizes the fuzzy performance index. Here, the fractional derivative is described in the Caputo sense. To find the solution, first we state some definitions and prove some required theorems. Then, we employ the obtained result to determine the necessary conditions. Furthermore, we show that the obtained necessary optimality conditions become sufficient by considering some extra assumptions. Finally, some examples are presented for more illustration of the subject. |
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| AbstractList | This paper presents an extension to fractional optimal control problems with ambiguity. As the ambiguity is modeled with fuzzy method, we encounter with a fuzzy fractional optimal control problem. The objective in fuzzy fractional optimal control problem is to determine the best possible fuzzy control which satisfies the related fuzzy fractional dynamic systems and minimizes the fuzzy performance index. Here, the fractional derivative is described in the Caputo sense. To find the solution, first we state some definitions and prove some required theorems. Then, we employ the obtained result to determine the necessary conditions. Furthermore, we show that the obtained necessary optimality conditions become sufficient by considering some extra assumptions. Finally, some examples are presented for more illustration of the subject. |
| Author | Allahviranloo, T. Alinezhad, M. |
| Author_xml | – sequence: 1 givenname: M. surname: Alinezhad fullname: Alinezhad, M. email: alinezhad@phd.pnu.ac.ir organization: Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran – sequence: 2 givenname: T. surname: Allahviranloo fullname: Allahviranloo, T. email: tofigh@allahviranloo.com organization: Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran |
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| Keywords | Fuzzy fractional calculus Generalized Hakahara differentiability Fuzzy fractional derivative Fuzzy fractional differential equations Fuzzy fractional optimal control Fuzzy integral |
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| SubjectTerms | Fuzzy fractional calculus Fuzzy fractional derivative Fuzzy fractional differential equations Fuzzy fractional optimal control Fuzzy integral Generalized Hakahara differentiability |
| Title | On the solution of fuzzy fractional optimal control problems with the Caputo derivative |
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