Turnpike Properties for Mean-Field Linear-Quadratic Optimal Control Problems
Turnpike Properties for Mean-Field Linear-Quadratic Optimal Control Problems
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DOI：
10.1137/22m1524187
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发表时间：
2022-09
期刊：
影响因子：
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通讯作者：
Jingrui Sun;J. Yong
中科院分区：
文献类型：
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作者：
Jingrui Sun;J. Yong
研究了无穷时域上具有二次泛函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，（强）指数，积分，和均方收费公路的最佳对属性的建立。关键是正确地制定相应的静态优化问题，并找到方程确定的校正过程。这些都揭示了随机问题的主要特点，这是显着不同的确定性版本的理论。
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.