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

Articles in Press

Document Type : Research Article

Authors

• Rasoul Heydari Dastjerdi
• Ghasem Ahmadi

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

10.22067/ijnao.2024.86494.1380

Abstract

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.

Keywords

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

Main Subjects

• Control and Optimization

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