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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 7679165, 9 pages
Research Article

Optimal Preview Control for a Class of Linear Continuous Stochastic Control Systems in the Infinite Horizon

1School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
2Leeds Sustainability Institute, Leeds Beckett University, Leeds LS2 9EN, UK

Received 1 July 2016; Accepted 26 September 2016

Academic Editor: Andrzej Swierniak

Copyright © 2016 Jiang Wu 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 discusses the optimal preview control problem for a class of linear continuous stochastic control systems in the infinite horizon, based on the augmented error system method. Firstly, an assistant system is designed and the state equation is translated to the assistant system. Then, an integrator is introduced to construct a stochastic augmented error system. As a result, the tracking problem is converted to a regulation problem. Secondly, the optimal regulator is solved based on dynamic programming principle for the stochastic system, and the optimal preview controller of the original system is obtained. Compared with the finite horizon, we simplify the performance index. We also study the stability of the stochastic augmented error system and design the observer for the original stochastic system. Finally, the simulation example shows the effectiveness of the conclusion in this paper.