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Strong and weak solutions of fuzzy nonlinear optimal control problems via a Jacobi-based neural network scheme | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 اردیبهشت 1405 اصل مقاله (1.23 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.66698.3144 | ||
| نویسندگان | ||
| Aneseh Kazemi؛ Alireza Nazemi* | ||
| Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran. | ||
| چکیده | ||
| In this paper, an artificial neural network architecture is proposed for solving a class of fuzzy optimal control problems. At the first step, we consider the Pontryagin minimum principle for the mentioned problems. The necessary optimality conditions for these problems are stated in the form of two-point boundary value problems. Then, for the first time, a neural network solution method is introduced in which Jacobi functions are employed as activation functions in one of the hidden layers to approximate solutions to two-point boundary value problems. This neural network uses roots of Jacobi polynomials as the training dataset, and the Levenberg-Marquardt algorithm is chosen as the optimizer. By relying on the ability of the generalized fuzzy hyperbolic models as function approximator, the trial solutions of variables are substituted in the related two-point boundary value problem. The obtained algebraic nonlinear equations system is then reduced into an error function minimization problem. A learning scheme based on the Levenberg-Marquardt algorithm is employed as the optimizer to derive the adjustable parameters of fuzzy solutions. To show the effectiveness of the presented neural network, some numerical results are provided. | ||
| کلیدواژهها | ||
| Fuzzy optimal control؛ necessary optimality conditions؛ Jacobi neural network؛ Levenberg-Marquardt algorithm | ||
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آمار تعداد مشاهده مقاله: 45 تعداد دریافت فایل اصل مقاله: 62 |
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