Designing the sinc neural networks to solve the fractional optimal control problem

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 24 اردیبهشت 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.86494.1380

نویسندگان

Rasoul Heydari Dastjerdi^* ؛ Ghasem Ahmadi

Department of Applied Mathematics, Faculty of Mathematical Sciences, payame noor University, Tehran, Iran.

چکیده

Sinc numerical methods are essential approaches to solving nonlinear problems. In this work, based on this method, the sinc neural networks (SNNs) are designed and applied to solve the fractional optimal control problem (FOCP) in the sense of the Riemann–Liouville (RL) derivative. To solve the FOCP, we first approximate the RL derivative using Grunwald–Letnikov (GL) operators. Then, according to Pontryagin’s minimum principle (PMP) for FOCP and using an error function, we construct an unconstrained minimization problem. We approximate the solution of the ordinary differential equation obtained from the Hamiltonian condition using the sinc neural network. Simulation results show the efficiencies of the proposed approach.

کلیدواژه‌ها

Sinc numerical method؛ Neural network؛ Sinc neural network؛ Pontryagin’ s minimum principle؛ Fractional optimal control problem