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Mathematical Problems in Engineering
Volume 2017, Article ID 8521368, 8 pages
Research Article

Trajectory Optimization Based on Multi-Interval Mesh Refinement Method

1Air and Missile Defense College, Air Force Engineering University, Xi’an 710051, China
2School of Electronic and Information Engineering, Xi’an Jiao Tong University, Xi’an 710049, China

Correspondence should be addressed to Ningbo Li; moc.361@sal_bnl

Received 1 February 2017; Accepted 18 April 2017; Published 23 August 2017

Academic Editor: William MacKunis

Copyright © 2017 Ningbo Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In order to improve the optimization accuracy and convergence rate for trajectory optimization of the air-to-air missile, a multi-interval mesh refinement Radau pseudospectral method was introduced. This method made the mesh endpoints converge to the practical nonsmooth points and decreased the overall collocation points to improve convergence rate and computational efficiency. The trajectory was divided into four phases according to the working time of engine and handover of midcourse and terminal guidance, and then the optimization model was built. The multi-interval mesh refinement Radau pseudospectral method with different collocation points in each mesh interval was used to solve the trajectory optimization model. Moreover, this method was compared with traditional method. Simulation results show that this method can decrease the dimensionality of nonlinear programming (NLP) problem and therefore improve the efficiency of pseudospectral methods for solving trajectory optimization problems.