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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 6924324, 10 pages
Research Article

Optimal Preview Control for Discrete-Time Systems in Multirate Output Sampling

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

Received 9 August 2016; Accepted 22 September 2016

Academic Editor: Michele Brun

Copyright © 2016 Fucheng Liao and Yujian Guo. 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 studies the disturbance preview optimal control problem for discrete-time systems with multirate output sampling. By constructing the error system and using the discrete lifting technique, we reduce the multirate preview control problem to a single-rate one for a formal augmented system. Then, applying preview control theory, the optimal preview control law of the augmented error system is obtained. Meanwhile, we introduce a discrete integrator to eliminate the static error. Then we study a method to design a controller with preview action for the original system. And the existence conditions of the controller are also discussed in detail. Finally, numerical simulation is included to illustrate the effectiveness of the proposed method.