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A Stackelberg strategy for continuous-time mixed H2/H∞ control problem with time delay

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Abstract

This paper is concerned with the mixed H2/H∞ control with linear continuous time system and time delay. To deal with this, we presents a Stackelberg strategy by treating the control input and the disturbance as leader and follower, respectively. The leader’s control strategy minimizes the cost function which is in H2 norm and the follower’s control strategy maximizes the cost function which is in H∞ norm. The main technique of this paper is deal with the noncausal relationship of the variables caused by time delay in the control input by introducing two costates to capture the future information and one state to capture the past information. Through theory analyzing, the Stackelberg strategy exists uniquely. Moreover, with the assistance of the extended state space expression, the explicit expression of the strategy is obtained.

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Authors and Affiliations

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

    Xiaoqian Li, Wei Wang, Juanjuan Xu & Huanshui Zhang

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

Correspondence to Wei Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 61633014, 61573220, 61573221) and the Fundamental Research Funds of Shandong University (No. 2017JC009).

Xiaoqian Li received the B.Sc. degree in Automation Engineering from Shandong Agriculture University, Taian, China, in 2011, and the M.Sc. degree in Control Engineering from Northeastern University, Shenyang, China, in 2013. She is currently working toward the Ph.D. degree in Control Theory and Engineering at Shandong University, Jinan, China. Her research interests include optimal control, time-delay system, stabilization, and game theory.

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

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

Huanshui Zhang received the B.Sc. degree in Mathematics from the Qufu Normal University, Jining, China, in 1986 and the M.Sc. and Ph.D. degrees in Control Theory from Heilongjiang University, Harbin, China, and Northeastern University, Shenyang, China, in 1991 and 1997, respectively. He worked as a Postdoctoral Fellow at Nanyang Technological University from 1998 to 2001 and a Research Fellow at Hong Kong Polytechnic University from 2001 to 2003. He is currently a Changjiang Professor at Shandong University, Jinan, China. He has held Professorship in Harbin Institute of Technology from 2003 to 2006. He has also held visiting appointments as a Research Scientist and a 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. Dr. Zhang was an Associate Editor of the IEEE Transactions on Automatic Control, and the IEEE Transactions on Circuits and Systems I.

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Li, X., Wang, W., Xu, J. et al. A Stackelberg strategy for continuous-time mixed H2/H∞ control problem with time delay. Control Theory Technol. 16, 191–202 (2018). https://doi.org/10.1007/s11768-018-8014-4

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  • DOI: https://doi.org/10.1007/s11768-018-8014-4

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