Abstract
In this paper, the linear quadratic regulation problem for discrete-time systems with state delays and multiplicative noise is considered. The necessary and sufficient condition for the problem admitting a unique solution is given. Under this condition, the optimal feedback control and the optimal cost are presented via a set of coupled difference equations. Our approach is based on the maximum principle. The key technique is to establish relations between the costate and the state.
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This work was supported by the Taishan Scholar Construction Engineering by Shandong Government and the National Natural Science Foundation of China (Nos. 61120106011, 61203029).
Huanshui ZHANG graduated in Mathematics from the Qufu Normal University in 1986, and received his M.Sc. and Ph.D. degrees in Control Theory from Heilongjiang University, China, and Northeastern University, China, in 1991 and 1997, respectively. He worked as a postdoctoral fellow at Nanyang Technological University from 1998 to 2001 and Research Fellow at Hong Kong Polytechnic University from 2001 to 2003. He is currently a Changjiang Professorship at Shandong University, China. He held Professor in Harbin Institute of Technology from 2003 to 2006. He also held visiting appointments as Research Scientist and Fellow with Nanyang Technological University, Curtin University of Technology and Hong Kong City University from 2003 to 2006. His research interests include optimal estimation and control, time-delay systems, stochastic systems, signal processing and wireless sensor networked systems.
Lin LI received the B.Sc. and M.Sc. degrees in Pure Mathematics from Shandong University, Jinan, Shandong, China, in 2008 and 2011, respectively. She is currently pursuing the Ph.D. degree in Control Theory and Engineering at Shandong University. Her research interests include optimal control, stabilization, stochastic systems and time-delay systems.
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Li, L., Zhang, H. Linear quadratic regulation for discrete-time systems with state delays and multiplicative noise. Control Theory Technol. 13, 348–359 (2015). https://doi.org/10.1007/s11768-015-5036-z
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DOI: https://doi.org/10.1007/s11768-015-5036-z