论文标题
随机线性界面最佳控制问题的收费公路特性
Turnpike Properties for Stochastic Linear-Quadratic Optimal Control Problems
论文作者
论文摘要
本文将随机线性季度最佳控制问题的限制行为分为有限时间范围$ [0，t] $为$ t \ rightarrow \ infty $。在稳定性条件下，为这些问题建立了所谓的收费公路特性，该条件比可控性弱，通常在类似的问题中对普通微分系统的类似问题施加。在处理收费公路问题时，一个至关重要的问题是确定相应的静态优化问题。直观地模仿确定性情况，将漂移和扩散作为静态优化问题中的约束似乎很自然。但是，这将使我们走向错误的方向。发现正确的静态问题应包含扩散作为目标函数的一部分，这揭示了随机收费公路问题的深刻特征。
This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time horizon $[0,T]$ as $T\rightarrow\infty$. The so-called turnpike properties are established for such problems, under stabilizability condition which is weaker than the controllability, normally imposed in the similar problem for ordinary differential systems. In dealing with the turnpike problem, a crucial issue is to determine the corresponding static optimization problem. Intuitively mimicking deterministic situations, it seems to be natural to include both the drift and the diffusion as constraints in the static optimization problem. However, this would lead us to a wrong direction. It is found that the correct static problem should contain the diffusion as a part of the objective function, which reveals a deep feature of the stochastic turnpike problem.
