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Game theory approach to optimal control problem with multi-channel control

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Abstract

In this paper, we mainly study the optimal control problem with multi-channel control. The main contribution is to treat the optimal control problem as a leader-follower problem with multi-hierarchy decision makers in game theory. According to the sequence of the decision makers, the optimal controller is derived by the maximum principle. It is worth mentioning that the optimal solution is in the feedback form related to two symmetric Riccati equations with same dimension as the original state. Furthermore, the obtained solution is sufficient and necessary.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, Shandong, 250061, P. R. China

    Juanjuan Xu, Wei Wang & Huanshui Zhang

Authors
  1. Juanjuan Xu
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  2. Wei Wang
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  3. Huanshui Zhang
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Corresponding author

Correspondence to Wei Wang.

Additional information

Juanjuan Xu received her B.E. degree in Mathematics from the Qufu Normal University in 2006, and M.E. degree in Mathematics in 2009 from Shandong University, and her Ph.D. degree in Control Science and Engineering in 2013 from Shandong University, then postdoctoral research at the School of Control Science and Engineering, Shandong University. Her research interests include distributed consensus, optimal control, game theory, stochastic systems and time-delay systems.

Wei Wang received his Ph.D. degree in Control Science and Engineering from Shenzhen Graduate School, Harbin Institute of Technology, in 2010. He is currently a lecturer at Shandong University, Jinan Shandong, China. His research interests include optimal control and estimation for delayed systems, distributed control and estimation.

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 Heilong jiang 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 interests include optimal estimation and control, time-delay systems, stochastic systems, signal processing and wireless sensor networked systems.

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Xu, J., Wang, W. & Zhang, H. Game theory approach to optimal control problem with multi-channel control. Int. J. Control Autom. Syst. 13, 58–64 (2015). https://doi.org/10.1007/s12555-013-0023-y

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  • DOI: https://doi.org/10.1007/s12555-013-0023-y

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