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Journal of Control Science and Engineering
Volume 2013, Article ID 678679, 5 pages
Research Article

Solution to Singular Optimal Control by Backward Differential Flow

1Department of Mathematics, Tongji University, Shanghai 200092, China
2College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 28 October 2012; Revised 14 March 2013; Accepted 21 March 2013

Academic Editor: Mohamed Zribi

Copyright © 2013 Jinghao Zhu 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.


This paper presents a backward differential flow for solving singular optimal control problems. By using Krotov equivalent transformation, the cost functional is converted to a class of global optimization problems. Some properties of the flow are given to reveal the significant relationship between the dynamic of the flow and the geometry of the feasible set. The proposed method is also used in solving a class of variational problems. Some examples are illustrated.