SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 752-775, February 2024.
Abstract. This paper is concerned with an optimal control problem for a mean-field linear stochastic differential equation with a quadratic functional in the infinite time horizon. Under suitable conditions, including the stabilizability, the (strong) exponential, integral, and mean-square turnpike properties for the optimal pair are established. The keys are to correctly formulate the corresponding static optimization problem and find the equations determining the correction processes. These have revealed the main feature of the stochastic problems which are significantly different from the deterministic version of the theory.

中文翻译：

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平均场线性二次最优控制问题的收费公路特性

SIAM 控制与优化杂志，第 62 卷，第 1 期，第 752-775 页，2024 年 2 月。
摘要。本文研究无限时间范围内具有二次函数的平均场线性随机微分方程的最优控制问题。在适当的条件下，包括稳定性，建立了最佳对的（强）指数、积分和均方收费公路属性。关键是正确地表述相应的静态优化问题并找到确定修正过程的方程。这些揭示了随机问题的主要特征，与理论的确定性版本显着不同。