Stochastic optimization of a mixed moving average process for controlling non-Markovian streamflow environments
Stochastic optimization of a mixed moving average process for controlling non-Markovian streamflow environments
复制标题
用于控制非马尔可夫水流环境的混合移动平均过程的随机优化
DOI：
10.1016/j.apm.2022.11.009
复制
发表时间：
2023
影响因子：
5
通讯作者：
Hashiguchi Ayumi
中科院分区：
文献类型：
--
作者：
Yoshioka Hidekazu;Tanaka Tomohiro;Yoshioka Yumi;Hashiguchi Ayumi
研究了测度值仿射过程方差的费用约束静态遍历控制问题及其在流量管理中的应用。受控系统是一个跳跃驱动的混合移动平均过程，产生现实的次指数自相关函数，和“静态”性质的控制起源于一个现实的系统中的可观测性假设。马尔可夫提升被有效地用于离散系统到一个有限维的过程，这是更容易分析。该问题的解决是基于向后Kolmogorov方程和二次解的一个Anasterian。控制问题有一个封闭的形式的解决方案，方差有严格的上限和下限，这表明方差不能采取任意值，即使它是一个高的控制成本。讨论了基于马尔可夫提升的离散系统与原无穷维系统之间的对应关系。然后，一个收敛的马尔可夫提升被提出来近似的无限维系统。最后，将控制问题应用到真实的案例中，并对某河段进行了数据分析。一个扩展的问题受到一个额外的约束，保持流量的变化也进行了分析，而不会显着降低所提出的框架的易处理性。
We investigated a cost-constrained static ergodic control problem of the variance of measure-valued affine processes and its application in streamflow management. The controlled system is a jump-driven mixed moving average process that generates realistic subexponential autocorrelation functions, and the “static” nature of the control originates from a realistic observability assumption in the system. The Markovian lift was effectively used to discretize the system into a finite-dimensional process, which is easier to analyze. The resolution of the problem is based on backward Kolmogorov equations and a quadratic solution ansatz. The control problem has a closed-form solution, and the variance has both strict upper and lower bounds, indicating that the variance cannot take an arbitrary value even when it is subject to a high control cost. The correspondence between the discretized system based on the Markovian lift and the original infinite-dimensional one is discussed. Then, a convergent Markovian lift is presented to approximate the infinite-dimensional system. Finally, the control problem was applied to real cases using available data for a river reach. An extended problem subject to an additional constraint on maintaining the flow variability was also analyzed without significantly degrading the tractability of the proposed framework.