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- Title
Decentralized control for discrete-time mean-field systems with multiple controllers of delayed information.
- Authors
Qingyuan Qi; Zhiqiang Liu; Qianqian Zhang; Xinbei Lv
- Abstract
In this paper, the finite horizon asymmetric information linear quadratic (LQ) control problem is investigated for a discrete-time mean field system. Different from previous works, multiple controllers with different information sets are involved in the mean field system dynamics. The coupling of different controllers makes it quite difficult in finding the optimal control strategy. Fortunately, by applying the Pontryagin's maximum principle, the corresponding decentralized control problem of the finite horizon is investigated. The contributions of this paper can be concluded as follows: For the first time, based on the solution of a group of mean-field forward and backward stochastic difference equations (MF-FBSDEs), the necessary and sufficient solvability conditions are derived for the asymmetric information LQ control for the mean field system with multiple controllers. Furthermore, by the use of an innovative orthogonal decomposition approach, the optimal decentralized control strategy is derived, which is based on the solution to a non-symmetric Riccati-type equation.
- Subjects
PONTRYAGIN'S minimum principle; DISCRETE-time systems; STOCHASTIC difference equations; OPTIMAL control theory; MEAN field theory; INFORMATION asymmetry; ORTHOGONAL decompositions; INFORMATION resources management
- Publication
Asian Journal of Control, 2024, Vol 26, Issue 2, p753
- ISSN
1561-8625
- Publication type
Article
- DOI
10.1002/asjc.3250