A numerical method based on neural network approach for solving delay fractional optimal control problems

This paper presents a numerical approximation besed on neural network for solving delay fractional optimal control problems. The fractional derivative is described in the Caputo sense. The problem is first transformed, using a Padé approximation, to one without a time-delayed argument, Then we try to approximate the solution of Hamiltonian conditions based on the Pontryagin minimum principle (PMP). For this purpose, we use trial solutions for the states, Lagrange multipliers and control functions where these trial solutions are constructed by using two-layered perceptron, we then minimize the error function using a dynamic optimization method where weight and biases associated with all neurons are unknown. One numerical example is given to illustrate the effectiveness of the proposed scheme.

Keywords:

Delay fractional optimal control problem , Padé approximation , Hamiltonian conditions , Neural network , Error function , Dynamic optimization method