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Stackelberg Strategy of Two-player Stochastic Difference Game With Time Delay

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  • Control Theory and Applications
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Abstract

In this paper, we study the open-loop Stackelberg strategy of stochastic Stackelberg game with time delay. The main contribution is to give the explicit Stackelberg strategy in terms of Riccati equations. The key to solving the problem is the explicit solvability of the forward and backward stochastic difference equations (FBSDEs). Moreover, the optimal costs are indicated by using the initial value of the state.

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Authors and Affiliations

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

    Jingmei Liu, Wei Wang & Juanjuan Xu

  2. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266000, China

    Huanshui Zhang

Authors
  1. Jingmei Liu
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  2. Wei Wang
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Correspondence to Wei Wang.

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The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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This work was supported by the National Natural Science Foundation of China under Grants 61821004, 62250056, and the Natural Science Foundation of Shandong Province (ZR2021ZD14, ZR2021JQ24), and Science and Technology Project of Qingdao West Coast New Area (2019-32, 2020-20, 2020-1-4), High-level Talent Team Project of Qingdao West Coast New Area (RCTD-JC-2019-05), Key Research and Development Program of Shandong Province (2020CXGC01208).

Jingmei Liu received her B.S. and M.Sc. degrees in mathematics from Qufu Normal University, in 2015 and 2018, respectively. She is currently a doctoral student with the School of Control Science and Engineering, Shandong University, China. Her research interests include optimal control, 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 Professor with the School of Control Science and Engineering, Shandong University, China. His research interests include optimal control and estimation for delayed systems, distributed control and estimation.

Juanjuan Xu received her B.S. degree in mathematics from Qufu Normal University in 2006, an M.Sc. degree in mathematics from Shandong University in 2009, and a Ph.D. degree in control theory from Shandong University in 2013. She is currently a Professor with the School of Control Science and Engineering, Shandong University, China. Her research interests include distributed consensus, optimal control, game theory, stochastic systems, and time-delay systems.

Huanshui Zhang received his B.S. degree in mathematics from Qufu Normal University in 1986 and 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 Chinese University of Hong Kong and Hong Kong Polytechnic University from 2001 to 2003. From 1986 to 1999, he served as an Assistant and Associate Professor at Taishan College, China. He held a Professor at Shandong University, China, from 1999 to 2003. From 2003 to 2006, he served as a Professor at Harbin Institute of Technology, Shenzhen, China. From 2006 to 2019, he was a Taishan Professor and Changjiang Professor at Shandong University, China. He is currently a Distinguished Professor at Shandong University of Science and Technology, China. 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 and distributed control, time-delay systems, stochastic systems, and networked control systems. He was an Associate Editor of IEEE Transactions on Automatic Control, and IEEE Transactions on Circuits and Systems I.

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Liu, J., Wang, W., Xu, J. et al. Stackelberg Strategy of Two-player Stochastic Difference Game With Time Delay. Int. J. Control Autom. Syst. 21, 2904–2915 (2023). https://doi.org/10.1007/s12555-022-0534-5

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  • DOI: https://doi.org/10.1007/s12555-022-0534-5

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