A novel numerical method for solving optimal control problems using fourth-degree hat functions
This paper focuses on solving a class of nonlinear optimal control problems by constructing novel hat functions based on fourth-order polynomials, namely, fourth-degree hat functions (FDHFs). The FDHFs are used in this method to approximate the state equations and cost function. In fact, the FDHFs e...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818123000207 |
| _version_ | 1797797150478827520 |
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| author | Jehad K. Mohammed Ayad R. Khudair |
| author_facet | Jehad K. Mohammed Ayad R. Khudair |
| author_sort | Jehad K. Mohammed |
| collection | DOAJ |
| description | This paper focuses on solving a class of nonlinear optimal control problems by constructing novel hat functions based on fourth-order polynomials, namely, fourth-degree hat functions (FDHFs). The FDHFs are used in this method to approximate the state equations and cost function. In fact, the FDHFs enable us to turn the optimal control problem under consideration into a nonlinear optimal control problem with unknown coefficients that is easy to solve by any numerical method. The main advantages of the proposed method are its simplicity, ease of application, low computational expense, and avoidance of numerical integration. Several examples have been discussed to demonstrate the efficacy and applicability of the suggested method. |
| first_indexed | 2024-03-13T03:43:49Z |
| format | Article |
| id | doaj.art-a6ca5e3695794cbeb9057972c25d182e |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-03-13T03:43:49Z |
| publishDate | 2023-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-a6ca5e3695794cbeb9057972c25d182e2023-06-23T04:44:52ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812023-06-017100507A novel numerical method for solving optimal control problems using fourth-degree hat functionsJehad K. Mohammed0Ayad R. Khudair1Department of Mathematics, College of Education for Pure Science, University of Basrah, Basrah, IraqDepartment of Mathematics, College of Science, University of Basrah, Basrah, Iraq; Corresponding author.This paper focuses on solving a class of nonlinear optimal control problems by constructing novel hat functions based on fourth-order polynomials, namely, fourth-degree hat functions (FDHFs). The FDHFs are used in this method to approximate the state equations and cost function. In fact, the FDHFs enable us to turn the optimal control problem under consideration into a nonlinear optimal control problem with unknown coefficients that is easy to solve by any numerical method. The main advantages of the proposed method are its simplicity, ease of application, low computational expense, and avoidance of numerical integration. Several examples have been discussed to demonstrate the efficacy and applicability of the suggested method.http://www.sciencedirect.com/science/article/pii/S2666818123000207Fourth-degree hat functionsNonlinear optimal controlOperational matrixComputational method |
| spellingShingle | Jehad K. Mohammed Ayad R. Khudair A novel numerical method for solving optimal control problems using fourth-degree hat functions Partial Differential Equations in Applied Mathematics Fourth-degree hat functions Nonlinear optimal control Operational matrix Computational method |
| title | A novel numerical method for solving optimal control problems using fourth-degree hat functions |
| title_full | A novel numerical method for solving optimal control problems using fourth-degree hat functions |
| title_fullStr | A novel numerical method for solving optimal control problems using fourth-degree hat functions |
| title_full_unstemmed | A novel numerical method for solving optimal control problems using fourth-degree hat functions |
| title_short | A novel numerical method for solving optimal control problems using fourth-degree hat functions |
| title_sort | novel numerical method for solving optimal control problems using fourth degree hat functions |
| topic | Fourth-degree hat functions Nonlinear optimal control Operational matrix Computational method |
| url | http://www.sciencedirect.com/science/article/pii/S2666818123000207 |
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