A Numerical Approach for Solving Nonlinear Optimal Control Problems Using the Hybrid Scheme of Fitness Dependent Optimizer and Bernstein Polynomials
In this paper, a heuristic scheme based on the hybridization of Bernstein Polynomials (BPs) and nature-inspired optimization techniques is presented to achieve the numerical solution of Nonlinear Optimal Control Problems (NOCPs) efficiently. The solution of NOCP is approximated by the linear combina...
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| Format: | Article |
| Language: | English |
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IEEE
2022-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9770805/ |
| _version_ | 1817989854309384192 |
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| author | Ghulam Fareed Laghari Suheel Abdullah Malik Amil Daraz Azmat Ullah Tamim Alkhalifah Sheraz Aslam |
| author_facet | Ghulam Fareed Laghari Suheel Abdullah Malik Amil Daraz Azmat Ullah Tamim Alkhalifah Sheraz Aslam |
| author_sort | Ghulam Fareed Laghari |
| collection | DOAJ |
| description | In this paper, a heuristic scheme based on the hybridization of Bernstein Polynomials (BPs) and nature-inspired optimization techniques is presented to achieve the numerical solution of Nonlinear Optimal Control Problems (NOCPs) efficiently. The solution of NOCP is approximated by the linear combination of BPs with unknown coefficients. The unknown coefficients are estimated by transforming the NOCP into an error minimization problem and formulating the objective function. The Genetic Algorithm (GA) and Fitness Dependent Optimizer (FDO) are used for solving the objective function and obtaining the optimum values of the unknown coefficients. The findings and statistical results indicate the represented hybrid scheme offers encouraging results and outperforms the most recent and popular methods proposed in the literature, which ultimately validates the efficacy and productivity of the recommended approach. Furthermore, statistical analysis is incorporated to examine the reliability and stability of the suggested technique. Consequently, the remarkable difference is evident in simplicity, flexibility, and effectiveness compared to the other methods considered. |
| first_indexed | 2024-04-14T00:52:26Z |
| format | Article |
| id | doaj.art-3d4efdd469104f608b2a318301df3c73 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-14T00:52:26Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-3d4efdd469104f608b2a318301df3c732022-12-22T02:21:45ZengIEEEIEEE Access2169-35362022-01-0110502985031310.1109/ACCESS.2022.31732859770805A Numerical Approach for Solving Nonlinear Optimal Control Problems Using the Hybrid Scheme of Fitness Dependent Optimizer and Bernstein PolynomialsGhulam Fareed Laghari0https://orcid.org/0000-0002-9084-4674Suheel Abdullah Malik1https://orcid.org/0000-0002-6108-5090Amil Daraz2https://orcid.org/0000-0002-5532-9175Azmat Ullah3https://orcid.org/0000-0002-4519-5222Tamim Alkhalifah4https://orcid.org/0000-0001-8407-2068Sheraz Aslam5https://orcid.org/0000-0003-4305-0908Department of Electrical Engineering, Faculty of Engineering and Technology, International Islamic University Islamabad (IIUI), Islamabad, PakistanDepartment of Electrical Engineering, Faculty of Engineering and Technology, International Islamic University Islamabad (IIUI), Islamabad, PakistanDepartment of Electrical Engineering, Faculty of Engineering and Technology, International Islamic University Islamabad (IIUI), Islamabad, PakistanOil and Gas Development Company Ltd. (OGDCL), Islamabad, PakistanDepartment of Computer, College of Science and Arts, Qassim University, Ar Rass, Qassim, Saudi ArabiaDepartment of Electrical Engineering, Computer Engineering and Informatics, Cyprus University of Technology, Limassol, CyprusIn this paper, a heuristic scheme based on the hybridization of Bernstein Polynomials (BPs) and nature-inspired optimization techniques is presented to achieve the numerical solution of Nonlinear Optimal Control Problems (NOCPs) efficiently. The solution of NOCP is approximated by the linear combination of BPs with unknown coefficients. The unknown coefficients are estimated by transforming the NOCP into an error minimization problem and formulating the objective function. The Genetic Algorithm (GA) and Fitness Dependent Optimizer (FDO) are used for solving the objective function and obtaining the optimum values of the unknown coefficients. The findings and statistical results indicate the represented hybrid scheme offers encouraging results and outperforms the most recent and popular methods proposed in the literature, which ultimately validates the efficacy and productivity of the recommended approach. Furthermore, statistical analysis is incorporated to examine the reliability and stability of the suggested technique. Consequently, the remarkable difference is evident in simplicity, flexibility, and effectiveness compared to the other methods considered.https://ieeexplore.ieee.org/document/9770805/Optimal control problemsoptimization problemBernstein polynomialsfitness dependent optimizergenetic algorithm |
| spellingShingle | Ghulam Fareed Laghari Suheel Abdullah Malik Amil Daraz Azmat Ullah Tamim Alkhalifah Sheraz Aslam A Numerical Approach for Solving Nonlinear Optimal Control Problems Using the Hybrid Scheme of Fitness Dependent Optimizer and Bernstein Polynomials IEEE Access Optimal control problems optimization problem Bernstein polynomials fitness dependent optimizer genetic algorithm |
| title | A Numerical Approach for Solving Nonlinear Optimal Control Problems Using the Hybrid Scheme of Fitness Dependent Optimizer and Bernstein Polynomials |
| title_full | A Numerical Approach for Solving Nonlinear Optimal Control Problems Using the Hybrid Scheme of Fitness Dependent Optimizer and Bernstein Polynomials |
| title_fullStr | A Numerical Approach for Solving Nonlinear Optimal Control Problems Using the Hybrid Scheme of Fitness Dependent Optimizer and Bernstein Polynomials |
| title_full_unstemmed | A Numerical Approach for Solving Nonlinear Optimal Control Problems Using the Hybrid Scheme of Fitness Dependent Optimizer and Bernstein Polynomials |
| title_short | A Numerical Approach for Solving Nonlinear Optimal Control Problems Using the Hybrid Scheme of Fitness Dependent Optimizer and Bernstein Polynomials |
| title_sort | numerical approach for solving nonlinear optimal control problems using the hybrid scheme of fitness dependent optimizer and bernstein polynomials |
| topic | Optimal control problems optimization problem Bernstein polynomials fitness dependent optimizer genetic algorithm |
| url | https://ieeexplore.ieee.org/document/9770805/ |
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