An RBF collocation method for solving optimal control problems

A direct solution to optimal control problems is introduced based on interpolating global radial basis functions (RBFs) on arbitrary collocation points. In the proposed approach, called the RBF collocation method, states and controls are parameterized with any arbitrary global RBF and the continuous-time optimal control problem is discretized using arbitrary collocation points to transcribe it into a nonlinear programming problem. Numerical examples including a multiple UAV navigation problem are provided to evaluate the performance of the proposed method. It is shown that the RBF collocation method is more accurate and also computationally more efficient than a local polynomial (B-spline) method and a global polynomial (Legendre pseudospectral) method for the UAV navigation problem. The fact that RBF method can employ a variety of RBF functions for the interpolation and also a wide range of arbitrary nodes for the discretization means that the proposed method offers a very flexible RBF framework for direct trajectory optimization. The numerical results confirm the efficiency of the proposed method for solving optimal control problems.