论文标题
用于无限二维随机微分方程的积分运算符Riccati方程的集成运算符的建模和计算
Modeling and computation of an integral operator Riccati equation for an infinite-dimensional stochastic differential equation governing streamflow discharge
论文作者
论文摘要
我们提出了通过优化无限二级跳跃驱动随机微分方程（SDE）的线性季度控制问题（LQ）控制问题。我们的SDE是Ornstein-Uhlenbeck过程（SUPOU过程）的叠加，生成了在实际数据中观察到的次指定自相关函数。积分操作符Riccati方程是通过启发性得出的，以确定无限维系统的最佳控制。此外，其有限尺寸版本是通过回归速度的离散分布得出的，并通过有限差方案计算。通过验证参数分析了riccati方程的最佳性。根据多年生河的实际数据，将SUPOU工艺进行参数化。通过计算实验分析了数值方案的收敛性。最后，我们证明了所提出的模型在现实问题中的应用以及Kolmogorov向后方程进行控制的性能评估。
We propose a linear-quadratic (LQ) control problem of streamflow discharge by optimizing an infinite-dimensional jump-driven stochastic differential equation (SDE). Our SDE is a superposition of Ornstein-Uhlenbeck processes (supOU process), generating a sub-exponential autocorrelation function observed in actual data. The integral operator Riccati equation is heuristically derived to determine the optimal control of the infinite-dimensional system. In addition, its finite-dimensional version is derived with a discretized distribution of the reversion speed and computed by a finite difference scheme. The optimality of the Riccati equation is analyzed by a verification argument. The supOU process is parameterized based on the actual data of a perennial river. The convergence of the numerical scheme is analyzed through computational experiments. Finally, we demonstrate the application of the proposed model to realistic problems along with the Kolmogorov backward equation for the performance evaluation of controls.
