A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations in Infinite Horizon

Key Points

• The central aim is to explore the linear-quadratic optimal control problem in mean-field stochastic differential equations over an infinite horizon.
• Analyzed the stabilizability of the control system
• Investigated well-posedness of the linear-quadratic problem
• Expressed optimal control as a linear state feedback
• Examined solutions of two algebraic Riccati equations
• Applied semi-definite programming methods for solvability analysis.
• Demonstrated conditions for the stabilizability of the control system.
• Established well-posedness of the linear-quadratic optimal control problem.
• Achieved expressible optimal control through state feedback and mean calculations.

Abstract