Discontinuous Galerkin optimal control for constrained nonlinear problems

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 for bang-bang optimal control problems, discontinuous element-based Galerkin techniques lead to improved solution accuracies. Also, we show that the Galerkin optimal control method has the potential to reduce the dimension of multi-scale problems. Using two examples, the Galerkin method described in this paper is shown to be a very accurate and highly versatile method.