Xun Pan's research while affiliated with Northwestern Polytechnical University and other places

Publications (2)

Article
Solving minimum-time low-thrust orbital transfer problems in the three-body problem by indirect methods is an extremely difficult task, which is mainly due to the small convergence domain of the optimal solution and the highly nonlinear nature associated with the three-body problem. Homotopy methods, the principle of which is to embed a given probl...
Article
Full-text available
Finding a solution to a low-thrust minimum-fuel transfer trajectory optimization problem in the circular restricted three-body problem (CRTBP) is already known to be extremely difficult due to the strong nonlinearity and the discontinuous bang-bang control structure. What is less commonly known is that such a problem can have many local solutions t...

Citations

... There are multiple approaches to define the sequence of neighboring OCPs, for instance, by 1) modifying the nonlinear part of the dynamics (i.e., the acceleration due to the central body) 8,9 or by removing (or attenuating) nonlinear terms to define a simpler starting problem, 10 2) modifying the boundary conditions from those available solutions, swept to the boundary condition of interest, 11,12 3) modifying the running cost by introducing quadratic/logarithmic terms such that an easier problem is first solved, 13, 14 4) altering the dynamics by introducing error terms 15 or introducing both error and error-control terms, 16 5) applying smoothing methods directly to the admissible control input using the hyperbolic tangent smoothing (HTS) method, 17 6) the unified trigonometrization method (UTM) 18 and 7) parametric bounding homotopy methods. 19,20 UTM is the most advanced trigonometry-based regularization method and has been applied to: complex atmospheric flight OCPs; 21 mars entry, descent and landing problems; 22 and low-thrust trajectory optimization problems. 23 In this paper, our focus is on approaches that use control regularization and smoothing techniques. ...
... Homotopy method [17] shows good convergency, but the solving process could be time-consuming by using an arbitrary initial approximation. Direct transform method [18] converts BVP into IVPs, but it is not a universally valid approach. ...