Galerkin Optimal Control

This paper introduces a family of computational methods for solving optimal control problems that calculate optimal trajectories using Galerkin numerical techniques. An important result in the theoretical foundation of these methods is that their associated feasibility and consistency theorems are proved for problems with continuous and/or piecewise continuous controls. In this paper we demonstrate that Galerkin numerical techniques allow for the formulation of optimal control problems in a number of ways that allow for efficiency and/or improved accuracy. The family of Galerkin methods presented can solve a wide range of optimal control problems with a variety of state and control constraints. Numerical formulations using Lagrangian and Legendre test functions are derived. Finally, numerical examples demonstrate the versatile nature of various Galerkin optimal control formulations.