Modeling and computation of an integral operator Riccati equation for an infinite-dimensional stochastic differential equation governing streamflow discharge
Modeling and computation of an integral operator Riccati equation for an infinite-dimensional stochastic differential equation governing streamflow discharge
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DOI：
10.1016/j.camwa.2022.09.009
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发表时间：
2022-04
期刊：
影响因子：
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通讯作者：
H. Yoshioka;M. Tsujimura;Tomohiro Tanaka;Y. Yoshioka;Ayumi Hashiguchi
中科院分区：
文献类型：
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作者：
H. Yoshioka;M. Tsujimura;Tomohiro Tanaka;Y. Yoshioka;Ayumi Hashiguchi
通过优化无穷维跳驱动的随机微分方程，提出了一个线性二次型流量控制问题。我们的自相关函数是Ornstein-Uhlenbeck过程（supplemental过程）的叠加，产生在实际数据中观察到的次指数自相关函数。积分算子Riccati方程的推导，以确定无限维系统的最优控制。此外，它的有限维版本推导出离散化的反转速度分布和计算的有限差分格式。Riccati方程的最优性分析的验证参数。根据多年河流的实际资料，对补给过程进行了参数化。通过数值实验分析了该数值格式的收敛性。最后，我们展示了应用所提出的模型，以现实的问题，沿着与柯尔莫哥洛夫向后方程的控制性能评估。
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.