Fractional infinite-horizon optimal control problems with a feed forward neural network scheme

摘要

This paper presents a method based on neural networks to solve fractional infinite-horizon optimal control problems s(FIHOCP)s, where the dynamic control system depends on Caputo fractional derivatives. First, with the help of an approximation, the Caputo derivative is replaced to integer-order derivative. Using a suitable change of variable, the IHOCP is transformed into a finite-horizon one. According to the Pontryagin minimum principle (PMP) for optimal control problems and by constructing an error function, an unconstrained minimization problem is defined. In the optimization problem, the trial solutions are used for state, costate and control functions where these trial solutions are constructed by using two-layered perceptron neural network. Two numerical results are introduced to explain our main results.