Discrete‐time indefinite mean field linear quadratic games with multiplicative noise

This paper considers discrete‐time mean field linear quadratic games with multiplicative noises, where the weighting matrices in the cost functions are allowed to be indefinite. First, by expanding the dimension of the systems, we present the necessary and sufficient condition for the existence of N...

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Bibliographic Details
Published in:Asian journal of control 2024-03, Vol.26 (2), p.626-635
Main Authors: Ma, Xiao, Wang, Bing‐Chang, Zhang, Huanshui
Format: Article
Language:English
Subjects:
Cost function
Decentralized control
Game theory
Games
Mathematical analysis
Optimal control
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Summary:This paper considers discrete‐time mean field linear quadratic games with multiplicative noises, where the weighting matrices in the cost functions are allowed to be indefinite. First, by expanding the dimension of the systems, we present the necessary and sufficient condition for the existence of Nash equilibrium. Second, by solving the limiting optimal control problem, we design a set of decentralized control strategies, which is shown to be an ‐Nash equilibrium. Finally, a numerical example is given to illustrate the effectiveness of the proposed control strategies.
ISSN:1561-8625
1934-6093
DOI:10.1002/asjc.3026