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A High-Precision Single Shooting Method for Solving Hypersensitive Optimal Control Problems
Joint Authors
Pan, Binfeng
Wang, Yang
Tian, Shaohua
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-04-15
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Pan, Binfeng& Wang, Yang& Tian, Shaohua. 2018. A High-Precision Single Shooting Method for Solving Hypersensitive Optimal Control Problems. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1209048
Modern Language Association (MLA)
Pan, Binfeng…[et al.]. A High-Precision Single Shooting Method for Solving Hypersensitive Optimal Control Problems. Mathematical Problems in Engineering No. 2018 (2018), pp.1-11.
https://search.emarefa.net/detail/BIM-1209048
American Medical Association (AMA)
Pan, Binfeng& Wang, Yang& Tian, Shaohua. A High-Precision Single Shooting Method for Solving Hypersensitive Optimal Control Problems. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1209048
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1209048