随机线性-二次方最优控制问题的长期行为

Jiamin Jian, Sixian Jin, Qingshuo Song, Jiongmin Yong
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摘要

本文研究了线性二次随机最优控制问题解的渐近行为。本文首次引入了所谓的概率细胞问题。它是对哈密尔顿-雅可比方程同质化中著名的单元问题的概率解释。通过建立该问题与遍历代价问题之间的联系,我们从不同角度揭示了线性-二次随机最优控制问题的拐点特性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Long-Time Behaviors of Stochastic Linear-Quadratic Optimal Control Problems
This paper investigates the asymptotic behavior of the solution to a linear-quadratic stochastic optimal control problems. The so-called probability cell problem is introduced the first time. It serves as the probability interpretation of the well-known cell problem in the homogenization of Hamilton-Jacobi equations. By establishing a connection between this problem and the ergodic cost problem, we reveal the turnpike properties of the linear-quadratic stochastic optimal control problems from various perspectives.
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