Iterative Solution of Nonlinear Optimal Control Problems

The solution of nonlinear, state-constrained, discrete optimal control problems by mathematical programming methods is described. The iterative solution consists essentially of Newton’s method with a convex (or linear) programming problem solved at each iteration. Global convergence of the iterative method is demonstrated provided a convexity and constraint set condition are both satisfied. The computational solution of nonlinear equation control problems makes use of a previously developed method for state-constrained linear equation problems. The solution method for nonlinear problems is illustrated by means of two numerical examples.