Survey of Two Classes of Continuation Methods for Solving Optimal Bang-Bang Control of Low-Thrust Space Trajectories

Abstract

The optimal Bang-Bang control problem of low-thrust space trajectories is introduced. Two classes of continuation methods are described：the first solves the energy-optimal solution，and subsequently employs the energy-fuel homotopy to obtain the optimal Bang-Bang control；the second introduces a switching principle，and obtains the optimal Bang-Bang control through parameter continuation starting from a two-impulse solution. The two continuation methods are compared，and the advantages and characteristics of the two methods are discussed. The prospects of the continuation methods applying to more complicated low-thrust trajectory designs are proposed. The concept of artificial intelligence trajectory optimization is presented，which contains three aspects：initial solution，continuation，and patching.

Keywords

low thrust / numerical optimization / Bang-Bang control / homotopy continuation / artificial intelligence