The numerical solution of control optimization problems by a systematic search in initial costate space

A method is presented for the numerical solution of control optimization problems by a systematic search in initial costate space. A three-stage search is conducted on the surface of a hypersphere. The first stage is a steepest descent search for an initial costate for which the terminal constraints are satisfied, and the second stage is a projected gradient search within the constraint set for the minimum of the performance function. For the third stage two different algorithms are developed which have good final convergence. A Newton-Raphson method is applied to a projected transversality error, and a projected gradient method is developed which allows standard gradient acceleration and nonlinear programming methods to be employed.