GENETIC ALGORITHM APPROACH FOR OPTIMAL-CONTROL PROBLEMS WITH LINEARLY APPEARING CONTROLS

For optimal control problems in Mayer form with all controls appearing only Linearly in the equations of motion, this paper presents a method for calculating the optimal Solution without user-specified initial guesses and without a priori knowledge of the optimal switching structure. The solution is generated in a sequence of steps involving a genetic algorithm (GA), nonlinear programming, and (multiple) shooting, The centerpiece of this method is a variant of the GA that provides reliable initial guesses for the nonlinear programming method, even for large numbers of parameters. As a numerical example, minimum-time spacecraft reorientation trajectories are generated. The described procedure never failed to correctly determine the optimal solution.