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

Abstract

Sinc numerical methods are essential approaches for 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 operators. Then, according to Pontryagin’s minimum principle 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 SNN. 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