Exact controllability of linear mean‐field stochastic systems and observability inequality for mean‐field backward stochastic differential equations. Issue 1 (23rd September 2020)

• Record Type: Journal Article
• Authors: Ye, Wenjie; Yu, Zhiyong
• Is Part Of: Asian journal of control. Volume 24:Issue 1(2022)
• Page Start: 237
• Page End: 248
• Publication Date: 2020-09-23
• Subjects: exact controllability -- forward‐backward stochastic differential equation -- mean‐field stochastic system -- norm optimal control -- observability inequality; Automatic control -- Periodicals; Control theory -- Periodicals; 629.805
• DOI: 10.1002/asjc.2443
• Languages: English
• ISSNs: 1561-8625

Abstract

Abstract: This paper is concerned with the exact controllability of linear mean‐field stochastic systems with time‐variant random coefficients. We prove that the exact controllability, the validity of the observability inequality for the dual equation, the unique solvability of a family of optimal control problems, the unique solvability of a family of mean‐field forward‐backward stochastic differential equations (MF‐FBSDEs), and the unique solvability of a family of norm optimal control problems are all equivalent. Therefore, some approaches are provided to investigate the issue of exact controllability.