Fractional Optimal Control Problems with Neural Network Approach

This paper deals with a numerical technique for fractional optimal control problems (FOCPs) based on a neural network scheme. According to the Pontryagin minimum principle (PMP) for FOCPs and by constructing an error function, we define an unconstrained minimization problem. In the optimization problem, we use trial solutions for the state, costate and control functions where these trial solutions are constructed by using two- layered perceptron. We then minimize the error function where weights and biases associated with all neurons are unknown. Substituting the optimal values of the weights and biases in the trial solutions, we obtain the optimal solution of the original problem.