Comparing and analyzing min-time and min-effort criteria for free true anomaly of low-thrust orbital maneuvers with new optimal control algorithm

This research presents a new algorithm for solving optimal control problems with regard to path planning with a free initial condition. To conduct research in this subject, issues such as optimal control theory, orthogonal functions in the Hilbert space, and the evolutionary optimizations such as Genetic algorithm (GA), Particle swarm optimization (PSO), Genetic algorithm-Particle swarm optimization (GA-PSO) and Imperial competition algorithm (ICA) are utilized. The algorithm is proposed for low-thrust orbital transfer problems, which include nonlinear dynamic equations. To validate the algorithm, Edelbaum low-thrust equations are compared with proposed analytical solutions. Afterwards, the algorithm is investigated for low-thrust orbital transfers concerning equinoctial equations of the min-time and min-effort problems and compared with pseudo-spectral method. Also two performance indices are compared from the viewpoint of space mission analysis and design. In addition, to obtain the best point for starting maneuvers, initial condition of true anomaly is considered to be free. Once the orbital transfer problem is solved, the fuzzy decision maker has to choose the best configuration among the free true anomaly solutions and performance indices to upgrade the proposed algorithm. This configuration balanced two performance indices by considering free true anomaly. As a result, this novel algorithm is able to overcome difficulties of optimal control problems using the global optimization and multi combination performance indices. Another innovation of this new method in the field of optimal control theory is to set initial conditions with more than one performance criterion free.