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Mathematical Problems in Engineering
Volume 2015, Article ID 423580, 8 pages
Research Article

Application of the Preview Control Method to the Optimal Tracking Control Problem for Continuous-Time Systems with Time-Delay

School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Received 10 March 2015; Revised 27 July 2015; Accepted 2 August 2015

Academic Editor: Asier Ibeas

Copyright © 2015 Fucheng Liao and Haishan Xu. 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 considers the application of the preview control method to the optimal tracking control problem for a class of continuous-time systems with state and input delays. First, through a transformation, the system is transformed into a nondelayed one. Then, the tracking problem of the time-delay system is transformed into one of a nondelayed system via processing of the reference signal. We then apply preview control theory to derive an augmented system for the nondelayed system and design a controller with preview function assuming that the reference signal is previewable. Finally, we obtain the optimal control law of the augmented error system and thus obtain that of the original system by letting the preview length of the reference signal go to zero. Numerical simulations are provided to illustrate the effectiveness and validity of our conclusions.