Discrete‐time mean‐field stochastic linear‐quadratic optimal control problem with finite horizon. Issue 2 (11th March 2020)

• Record Type: Journal Article
• Authors: Song, Teng; Liu, Bin
• Is Part Of: Asian journal of control. Volume 23:Issue 2(2021)
• Page Start: 979
• Page End: 989
• Publication Date: 2020-03-11
• Subjects: discrete‐time -- generalized difference Riccati equations -- indefinite stochastic LQ control -- maximum principle -- mean‐field theory; Automatic control -- Periodicals; Control theory -- Periodicals; 629.805
• DOI: 10.1002/asjc.2306
• Languages: English
• ISSNs: 1561-8625

Abstract

Abstract: In this paper we consider the discrete‐time mean‐field stochastic linear‐quadratic (MF‐LQ) optimal control problem with indefinite weighting matrices. First, we establish the maximum principle, and by the solvability of mean‐field forward‐backward stochastic difference equations derived from the maximum principle, we characterize the existence of the open‐loop optimal control for the MF‐LQ problem. Then, by virtue of introducing the linear matrix inequalities condition, we obtain the solvability of the generalized difference Riccati equations (GDREs). Moreover, we show that the indefinite MF‐LQ problem is well‐posed if and only if the GDREs are solvable. Finally, a numerical example is used to show the effectiveness of the obtained results.