论文标题
多尺度线性二次随机最佳控制与乘法噪声
Multiscale Linear-Quadratic Stochastic Optimal Control With Multiplicative Noise
论文作者
论文摘要
我们研究了有限的时间范围线性界面最佳控制问题的渐近性能，该问题由多尺度随机过程带有乘法性布朗噪声。我们通过考虑相关的差异方程来解决问题，并将其重新定义为经典和确定性的奇异扰动问题。该确定性问题的渐近特性可以从众所周知的Tikhonov定理中收集。因此，我们能够提出两种近似方法，以实现随机最佳控制问题的价值函数。第一个是构造大约最佳的控制过程，而第二个是找到对值函数的直接限制。两种近似方法都依赖于具有某些稳定性属性的耦合微分 - 代数riccati方程的解决方案 - 这是本文的主要难度。
We investigate the asymptotic properties of a finite-time horizon linear-quadratic optimal control problem driven by a multiscale stochastic process with multiplicative Brownian noise. We approach the problem by considering the associated differential Riccati equation and reformulating it as a classical and deterministic singular perturbation problem. Asymptotic properties of this deterministic problem can be gathered from the well-known Tikhonov Theorem. Consequently, we are able to propose two approximation methods to the value function of the stochastic optimal control problem. The first is by constructing an approximately optimal control process whilst the second is by finding the direct limit to the value function. Both approximation methods rely on the existence of a solution to a coupled differential-algebraic Riccati equation with certain stability properties - this is the main difficulty of the paper.
