发表机构
Southern University of Science and Technology; Guilin University of Electronic Technology（南方科技大学; 桂林电子科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究后向结构线性平均场随机微分方程的精确可控性，建立Hautus准则，揭示零初始时刻与正初始时刻的二分性，并阐明相关ODE、SDE及平均场SDE系统间的可控性关系。
AI 中文摘要
本文研究具有后向结构的线性平均场随机微分方程的精确可控性。我们建立了Hautus准则，并揭示了零初始时刻与正初始时刻之间的尖锐二分性。在零时刻，精确可控性由平均动力学的Hautus条件刻画，且由中心化随机动力学产生额外的控制方向。在任何正初始时刻，精确可控性进一步要求中心化系统满足随机Hautus条件。与经典的基于特征向量的条件不同，该随机准则以相关Lyapunov型算子的半正定特征矩阵形式表述。该二分性源于初始σ-域的平凡性。我们还阐明了相应ODE、SDE和平均场SDE系统之间的可控性关系。
英文摘要
This paper studies exact controllability of linear mean-field stochastic differential equations with backward-structure. We establish Hautus criteria and uncover a sharp dichotomy between the zero initial time and positive initial times. At time zero, exact controllability is characterized by a Hautus condition for the mean dynamics, with additional control directions generated by the centered stochastic dynamics. At any positive initial time, exact controllability further requires a stochastic Hautus condition for the centered system. Unlike the classical eigenvector-based condition, this stochastic criterion is formulated in terms of positive-semidefinite eigenmatrices of an associated Lyapunov-type operator. The dichotomy arises from the triviality of the initial sigma-field. We also clarify the controllability relations among the corresponding ODE, SDE, and mean-field SDE systems.
