An Algorithm for the Iterative Solution of a Class of Two-Point Boundary Value Problems

The algorithm, which is based on second variations, is intended for a class of two-point boundary value problems arising in control optimization. These optimization problems are characterized by positive definite second variations, the absence of point constraints on control and state variables, and free-point terminal boundary conditions. In a suitably small neighborhood of the optimal trajectory, the algorithm gives one-step convergence within the limits of the accuracy obtained with numerical integration. The relationships which are used here and arise in variational mathematics are stated in an appendix.