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Mathematical Problems in Engineering
Volume 2018, Article ID 7908378, 11 pages
https://doi.org/10.1155/2018/7908378
Research Article

A High-Precision Single Shooting Method for Solving Hypersensitive Optimal Control Problems

1College of Astronautics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, China
2Department of Aerospace Engineering and Technology, Politecnico di Milano, 20156 Milano, Italy

Correspondence should be addressed to Binfeng Pan; nc.ude.upwn@gnefnibnap

Received 9 December 2017; Revised 27 February 2018; Accepted 12 March 2018; Published 15 April 2018

Academic Editor: Muhammad N. Akram

Copyright © 2018 Binfeng Pan 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.

Abstract

Solving hypersensitive optimal control problems is a long-standing challenge for decades in optimization engineering, mainly due to the possible nonexistence of the optimal solution to meet the required error tolerance under double-precision arithmetic and the hypersensitivity of the optimal solution with respect to the initial conditions. In this paper, a new high-precision single shooting method is presented to address the above two difficulties. Multiple-precision arithmetic and Taylor series method are introduced to provide the accurate optimal solution with arbitrary higher significant digits and arbitrary higher integral accuracy, respectively. Besides, a new modified bidirectional single shooting method is developed, which fully utilizes the three-segment structure of the hypersensitive optimal control problems and provides appropriate initial guess that is close to the optimal solutions. Numerical demonstrations in a typical hypersensitive optimal control problem are presented to illustrate the effectiveness of this new method, which indicates that the accurate optimal solution of this challenging problem can be easily solved by this simple single shooting method within several iterations.