Exact controllability of linear mean‐field stochastic systems and observability inequality for mean‐field backward stochastic differential equations
Wenjie Ye, Zhiyong Yu
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.
Topics & Concepts
ControllabilityObservabilityMathematicsStochastic differential equationApplied mathematicsNorm (philosophy)Field (mathematics)Stochastic partial differential equationMean field theoryMathematical analysisDifferential equationPure mathematicsPolitical sciencePhysicsQuantum mechanicsLawStability and Controllability of Differential EquationsStochastic processes and financial applicationsControl Systems and Identification