A Barrier Function Method for the Optimization of Trajectory Functionals with Constraints

We develop a barrier function method for the optimization of trajectory functionals with constraints. An approximate or relaxed barrier function is used to incorporate the trajectory constraints into an unconstrained trajectory functional that is minimized using a projection operator based Newton method. The proposed approach is a natural extension to infinite dimensions of the barrier function interior point method in convex optimization. The effectiveness of the approach is illustrated with minimum time optimal control problems under differing constraints