Analytical Initialization for Low-thrust Trajectory Optimization Based on Switching System

The traditional homotopy method usually transforms the low-thrust fuel-optimal control problem into the energy-optimal problem to increase the convergence rate of the indirect method. However, it is still necessary to guess the initial values of the co-states to initialize the solving algorithm. In this paper, the optimization model of the fuel-optimal problem is embedded in the switching system with the analytical initial co-states, which further improves the convergence rate with the analytical initialization. Firstly, the switching system is introduced with the embedded fuel-optimal problem. The switching function of the conventional switching system is derived from the optimal control, but in this paper, the given switching function is designed artificially to realize the switching and continuation among different systems. Secondly, based on the linearization technique, the target system is designed with analytical initial co-states, initializing the solving algorithm by a simple nominal trajectory. Finally, the numerical simulation verifies the effectiveness of the proposed method, which is more efficient than the traditional homotopy method.