Abstarct: Radial basis functions are a powerful tool for calculating approximate solutions in high dimensions and have an exponential convergence order and are independent of the network. In this thesis, a continuous-time optimal control problem is presented with some of the existing methods for solving these problems. Two direct methods baxsed on the interpolation of radial basis functions and arbitrary discretization are presented, including the local RBF method and the RBF-Galerkin method. Both methods use the selection of global RBFs as the interpolation function for the discretization points, and providing numerical examples shows the superiority of the two presented methods compared with other direct methods.