| An approach for solving optimal control problems based on the geometry of the reachable set is developed for linear systems with dissimilar actuators. This methodology is especially useful for problems which are optimally solved by discontinuous controls, though it is applicable to continuous control problems as well. In cases where multiple control actuators are available (and therefore very many combinations of actuators) the methodology naturally provides the optimal subset of actuators to be used for a given maneuver. This approach requires the optimization of a vector function which is only piecewise smooth. For very simple problems, the optimization can be done analytically, but for more complicated problems a numerical technique is necessary. A proof of the optimality of a general class of actuators is provided and several example problems are presented. Four different numerical techniques for optimization of nonsmooth cost functions are applied to the problem of optimal rendezvous and docking of two spacecraft. The four techniques are compared in terms of number of function evaluations required to solve the problem and quality of the solution found. |
