Issue |
ESAIM: COCV
Volume 29, 2023
|
|
---|---|---|
Article Number | 83 | |
Number of page(s) | 19 | |
DOI | https://doi.org/10.1051/cocv/2023060 | |
Published online | 08 November 2023 |
Stackelberg method to stabilize game-based control system
1
School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, PR China
2
School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, PR China
3
College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, Shandong 266590, PR China
4
Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao, Shandong 266237, PR China
* Corresponding author: hszhang@sdu.edu.cn
Received:
28
July
2022
Accepted:
13
August
2023
In this paper, we are concerned with the stabilization problem of the game-based control system. In particular, two players are involved in the system where one is to minimize the related cost function and the other is to stabilize the system. Different from the previous works, the new contribution is to derive the necessary and sufficient condition for the stabilization of the game-based control system by applying Stackelberg game method. The key technique is to explicitly solve the forward and backward difference equations (FBDEs) from the Stackelberg game and give the optimal feedback gain matrix of the leader by using the matrix maximum principle.
Mathematics Subject Classification: 49N10 / 91A65
Key words: FBDEs / game-based control system / stabilization / Stackelberg game
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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