Adaptive mesh refinement and collocation optimization method for solving non-smooth trajectory

被引：0
|
作者：
Pang W. [1 ]
Xie X. [1 ]
Liu Q. [1 ]
Liu J. [1 ]
机构：
[1] Department of Ordnance Science and Technology, Naval Aeronautical and Astronautical University, Yantai
来源：
Xi Tong Gong Cheng Yu Dian Zi Ji Shu/Systems Engineering and Electronics | 2017年 / 39卷 / 05期
关键词：
Collocation method; Mesh refinement; Non-smooth; Optimal control;
D O I：
10.3969/j.issn.1001-506X.2017.05.22
中图分类号：
学科分类号：
摘要：
The deficiencies of the traditional collocation method, such as the large number of meshes and collocation points, may cause the nonlinear equations to be computationally expensive and result in huge discrete errors. Due to these drawbacks of the traditional collocation method, an adaptive mesh refinement and collocation optimization method is proposed. Firstly, the optimization problem is transformed into the nonlinear programming problem in diffe-rent meshes. After implementing the Lagrange interpolation method to solve the optimization problem in these meshes, the absolute and relative errors are then obtained. Secondly, according to the magnitude of the trajectory curvature, the positions of non-smooth meshes are determined. Afterwards, the number of meshes and points are further determined by the relationship between the maximum relative error and the allowable error. Meanwhile, the number of collocation points is increased to enhance the solution accuracy in the case where the smooth meshes cannot satisfy the tolerance error. Finally, several numerical simulations are conducted to compare the proposed method with some other currently existing methods. The simulation results show that the collocation points and the number of meshes of the proposed method are less than those of the traditional adaptive mesh refinement methods. Moreover, the efficiency of the proposed method is higher than that of the traditional methods. © 2017, Editorial Office of Systems Engineering and Electronics. All right reserved.
引用
收藏
页码：1091 / 1099
页数：8
相关论文
共 18 条
  • [1] Yan X.L., Liao S.Y., Zhang J.S., Et al., Trajectory optimization using pseudospectral method based on a grid node refinement strategy, Journal of Astronautics, 34, 7, pp. 891-900, (2013)
  • [2] Zhao J.S., Gu L.X., She W.X., Application of local collocation method and mesh refinement to non-smooth trajectory optimization, Journal of Astronautics, 34, 11, pp. 1442-1450, (2013)
  • [3] Betts T.J., Huffman W., Mesh refinement in direct transcription methods for optimal control, Optimal Control Applications & Methods, 19, 1, pp. 1-21, (1998)
  • [4] Fahroo F., Ross M.I., Direct trajectory optimization by a chebyshev pseudospectral method, Journal of Guidance, Control, and Dynamics, 25, 1, pp. 160-166, (2002)
  • [5] Darby C.L., Hager W.W., Rao V.A., An hp-adaptive pseudospectral method for soluing optimal control problems, Optimal Control Applications and Methods, 32, 4, pp. 476-502, (2011)
  • [6] Zhang Y.A., Wang L.Y., Zhang G., Et al., A surrey of numerical methods for trajectory optimization, Journal of Naval Aeronautical and Astronautical University, 27, 5, pp. 481-486, (2012)
  • [7] Yang X.Y., Yang H.X., Wang P., Overview of pseudo-spectral method and its application in trajectory optimum design for flight vehicles, Journal of National University of Defense Technology, 37, 4, pp. 1-8, (2015)
  • [8] Jain D., Tsiotras P., Trajectory optimization using multiresolution techniques, Journal of Guidance, Control, and Dynamics, 35, 1, pp. 1425-1436, (2008)
  • [9] Wang L.Y., Zhang Y.A., Zhao G.R., Improved hp-adaptive mesh refinement algorithm and its application, Journal of Ballistics, 25, 1, pp. 16-21, (2013)
  • [10] Liu Y.B., Zhu H.W., Huang X.N., Et al., Optimal mesh segmentation algorithm for pseudospectral methods for non-smooth optimal control problems, Systems Engineering and Electronics, 35, 11, pp. 2396-2399, (2013)
12