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International Journal of Aerospace Engineering
Volume 2017 (2017), Article ID 9456179, 12 pages
Research Article

Variable-Time-Domain Online Neighboring Optimal Trajectory Modification for Hypersonic Interceptors

1Air and Missile Defence 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

Received 19 December 2016; Revised 24 April 2017; Accepted 8 June 2017; Published 12 July 2017

Academic Editor: Paul Williams

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.


The predicted impact point (PIP) of hypersonic interception changes continually; therefore the midcourse guidance law must have the ability of online trajectory optimization. In this paper, an online trajectory generation algorithm is designed based on neighboring optimal control (NOC) theory and improved indirect Radau pseudospectral method (IRPM). A trajectory optimization model is designed according to the features of operations in near space. Two-point boundary value problems (TPBVPs) are obtained based on NOC theory. The second-order linear form of transversality conditions is deduced backward to express the modifications of terminal states, costates, and flight time in terms of current state errors and terminal constraints modifications. By treating the current states and the optimal costates modifications as initial constraints and perturbations, the feedback control variables are obtained based on improved IRPM and nominal trajectory information. The simulation results show that when the changes of terminal constraints are not relatively large, this method can generate a modified trajectory effectively with high precision of terminal modifications. The design concept can provide a reference for the design of the online trajectory generation system of hypersonic vehicles.