A gradient-based optimization algorithm to solve optimal control problems with conformable fractional-order derivatives
In this paper, we solve numerically a class of fractional optimal control problems in the conformable sense. We first propose a nonlinear fractional optimal control problem subject to general equality and inequality constraints. Then, based on a novel numerical integration scheme, we present a discr...
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| Vydáno v: | Journal of computational and applied mathematics Ročník 454; s. 116169 |
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| Jazyk: | angličtina |
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Elsevier B.V
15.01.2025
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| ISSN: | 0377-0427 |
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| Abstract | In this paper, we solve numerically a class of fractional optimal control problems in the conformable sense. We first propose a nonlinear fractional optimal control problem subject to general equality and inequality constraints. Then, based on a novel numerical integration scheme, we present a discretization method for the governed fractional-order system as well as the cost and constraint functionals, which yields a discretized approximate problem. We further derive the gradients of the cost and constraint functionals in regard to the discretized controls. On the basis of this result, a numerical optimization approach to solve the approximate problem is developed. Finally, three non-trivial example problems are solved to illustrate the applicability and effectiveness of the developed approach. |
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| AbstractList | In this paper, we solve numerically a class of fractional optimal control problems in the conformable sense. We first propose a nonlinear fractional optimal control problem subject to general equality and inequality constraints. Then, based on a novel numerical integration scheme, we present a discretization method for the governed fractional-order system as well as the cost and constraint functionals, which yields a discretized approximate problem. We further derive the gradients of the cost and constraint functionals in regard to the discretized controls. On the basis of this result, a numerical optimization approach to solve the approximate problem is developed. Finally, three non-trivial example problems are solved to illustrate the applicability and effectiveness of the developed approach. |
| ArticleNumber | 116169 |
| Author | Gong, Zhaohua Liu, Chongyang Wu, Yonghong Teo, Kok Lay |
| Author_xml | – sequence: 1 givenname: Zhaohua surname: Gong fullname: Gong, Zhaohua organization: School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China – sequence: 2 givenname: Chongyang orcidid: 0000-0002-2229-6717 surname: Liu fullname: Liu, Chongyang email: chongyangliu@aliyun.com organization: School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China – sequence: 3 givenname: Kok Lay surname: Teo fullname: Teo, Kok Lay organization: School of Mathematical Sciences, Sunway University, Kuala Lumpur 47500, Malaysia – sequence: 4 givenname: Yonghong surname: Wu fullname: Wu, Yonghong organization: School of Electrical Engineering, Computing, and Mathematical Sciences, Curtin University, Perth 6845, Australia |
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| Keywords | Numerical integration Numerical optimization Optimal control Conformable fractional derivative |
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| Snippet | In this paper, we solve numerically a class of fractional optimal control problems in the conformable sense. We first propose a nonlinear fractional optimal... |
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| StartPage | 116169 |
| SubjectTerms | Conformable fractional derivative Numerical integration Numerical optimization Optimal control |
| Title | A gradient-based optimization algorithm to solve optimal control problems with conformable fractional-order derivatives |
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