Method of continuation for optimization of interplanetary low-thrust trajectories

The problem of local optimization of interplanetary low-thrust trajectories is considered with the use of the maximum principle and continuation numerical methods. Two types of problems are analyzed: problems with limited power and problems with limited thrust. The latter problem is generalized by introducing the dependence of thrust and specific impulse on available electric power. In order to reduce the problem of optimal control to a boundary value problem, the Pontryagin maximum principle is used, and then, using the continuation method, this boundary value problem is reduced to the Cauchy problem. Variants of the continuation method for optimizing low-thrust trajectories are presented in the paper, including a new method of continuation for the limited thrust problem, which does not require any choice of the initial approximation for boundary values of conjugate variables.