Abstarct: In this thesis a class of nonlinear optimal control problem with equality and inequality constrain is considered, and propose a new method baxsed on capabilities of artificial neural networks, in function approximation, to attain the solution of optimal control problems. To do so, we try to approximate the solution of Hamiltonian conditions baxsed on the Pontryagin minimum principle (PMP), then by constructing an error function, that contains all PMP conditions, we define an unconstrained minimization problem. In the proposed error function, we used trial solutions for the trajectory function, control function and the Lagrange multipliers. These trial solutions are constructed by using neurons. Then, we minimize the error function that contains just the weights of the trial solutions. Substituting the optimal values of the weights in the trial solutions, we obtain the optimal trajectory function, optimal control function and the optimal Lagrange multipliers.