Solving time delay fractional optimal control problems via a Gudermannian neural network and convergence results

In this paper, we propose a Gudermannian neural network scheme to solve optimal control problems of fractional-order system with delays in state and control. 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. We try to approximate the solution of the Hamiltonian conditions based on the Pontryagin minimum principle. 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 an unconstrained optimization scheme where weight and biases associated with all neurons are unknown. Some numerical examples are given to illustrate the effectiveness of the proposed method.