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Approximate Optimal Control Governed by some Parabolic Equations via Laguerre Polynomials Collocation Approach | ||
| International Journal of Industrial Electronics Control and Optimization | ||
| مقاله 3، دوره 9، شماره 1، خرداد 2026، صفحه 27-35 اصل مقاله (860.72 K) | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22111/ieco.2025.51086.1664 | ||
| نویسندگان | ||
| Yunes Mohamadi1؛ Maryam Alipour* 2؛ Akbar Hashemi Borzabadi3 | ||
| 1University of Sistan and Baluchestan, Zahedan, Iran. | ||
| 2Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran. | ||
| 3Faculty of Applied Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran. | ||
| چکیده | ||
| The present paper proposes a novel numerical approach for approximating solutions to optimal control problems with parabolic constraints. Utilizing Laguerre polynomials as a novel basis set, a method was developed to address a class of this problem. The employment of these basis functions in conjunction with the collocation method facilitates the transformation of optimal control problems governed by parabolic constraints into a system of nonlinear algebraic equations. The present study proposes an efficient discretization and transformation of complex optimal control problems governed by parabolic equations into lower-dimensional algebraic systems by leveraging the unique properties of Laguerre polynomials. Convergence analysis has been demonstrated to ascertain the optimal value approximations of the proposed method. In order to provide a comprehensive illustration of the reliability and applicability of the proposed method, two illustrative examples are presented. The findings underscore the efficacy and precision of the implemented methodology. This work makes a significant contribution to the field by offering a robust framework for solving complex parabolic control problems, thereby demonstrating the potential of spectral methods in the context of optimal control theory. | ||
| کلیدواژهها | ||
| optimal control problems with parabolic constraints؛ Laguerre polynomials؛ Spectral method؛ Collocation points؛ Convergence analysis. | ||
| مراجع | ||
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