Feasibility of the Galerkin optimal control method

A new numerical technique is presented for solving optimal control problems. This paper introduces a direct method that calculates optimal trajectories by discretizing the system dynamics using Galerkin numerical techniques and approximates the cost function with quadrature. We show that the Galerkin optimal control method with weak enforcement of boundary conditions leads to improved solution accuracies. Furthermore, we show that a feasible solution exists to the approximation of the constrained nonlinear optimal control problem. Using an example, the Galerkin method described in this paper is shown to be more accurate than some existing methods.