Function space quasi-Newton techniques with application to space shuttle trajectory optimization

Two existing function space quasi-Newton algorithms, Davidon and projected gradient, are modified so that they may handle directly control variable inequality constraints. A third quasi-Newton algorithm developed by C. G. Bryoden is extended to include optimal control problems. The Bryoden algorithm is further modified so that it may handle directly control variable inequality constraints. The quasi-Newton methods along with a steepest descent and two conjugate gradient algorithms are simulated on three relatively simple yet representative bounded control problems, two of which possess singular subarcs. Overall, the Broyden algorithm was found to be superior. The most notable result of the simulations was the clear superiority of the Broyden and Davidon algorithms in producing a sharp singular control subarc.