Mixed Optimization Approach for Low-Thrust Perturbed Rendezvous via Neural Networks

This study proposes a new model to combine the advantages of the indirect method, neural network, and evolutionary algorithm for the optimization of long-duration, low-thrust orbit rendezvous problems in low Earth orbits. The strategy of dividing the trajectory into three stages with fixed laws of thrust (the second stage keeps coasting without thrust) in the previous studies is inherited, in which the orbit changes of each stage are the decision variables and allocated evenly to each revolution. We derive a new simplified indirect method of the single-revolution transfer to replace the fixed-direction solution when evaluating the total velocity increment in the global optimization framework based on the differential evolution algorithm. Two neural networks are trained and applied to further accelerate the solving process. A correction algorithm for obtaining the trajectory and thrust laws of high-precision numerical dynamics is also proposed. The simulation results prove that the mixed model can obtain better solutions compared with previous methods because the simplified indirect method ensures the satisfaction of the first-order necessary condition. The neural networks can avoid the time-consuming shooting process of the indirect method and decrease the optimization time to less than 1 s. Moreover, the correction algorithm just requires five iteration steps to obtain the high-precision solution. The method can be applied for both approximate mission analysis and precise trajectory generation for orbit transfers in low Earth orbits.