Fractional infinite-horizon optimal control problems with a new definition of adaptive derivative and a feed forward neural networkscheme

This paper deals with the infinite-horizon optimal control problem of a fractional dynamic system(FIHOC) with a new definition of adaptive derivative. The form of the derivatives definition shows that it is the most natural definition. By a suitable change of variable, we transform the problem to a fractional finite-horizon optimal control problem (FFHOC) problem. Then according to the Pontryagin minimum principle (PMP) for optimal control problems and by constructing an error function, we define an unconstrained minimization problem. In the optimization problem, we use trial solutions for the state and control functions where these trial solutions are constructed by using two-layered perceptron neural network. An application is introduced to explain our main results.