Parametric optimization analysis for minimum-fuel low-thrust coplanar orbit transfer

A study of a model of precisewise continuous time functions, applied to approximate the optimal thrust control angle for minimum-fuel coplanar orbit transfers with constant low thrust from a near-Earth circular orbit was conducted. The second-order gradient method (SOGM) was used to determine the model of optimum thrust control and also to find a solution for the optimum orbit transfer problems. The optimal trajectories for the transfer between two orbits were solved using the SOGM method to establish a comprehensive model. It was found that after determining an optimal trajectory to transfer between the two close orbits, other control variable histories, including terminal time and the penalty coefficients of constraints can be used as a set of initial guesses for a new problem. Extensive studies have revealed that by assuming the control angle as two continuous time functions and a switch at time t1, the optimal trajectories could be characterized effectively.