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.

我们通过优化无限维跳跃驱动的随机微分方程 (SDE)，提出了一种水流排放的线性二次 (LQ) 控制问题。我们的 SDE 是 Ornstein-Uhlenbeck 过程（supOU 过程）的叠加，生成在实际数据中观察到的次指数自相关函数。启发式推导积分算子Riccati方程以确定无限维系统的最优控制。此外，它的有限维版本是通过回归速度的离散分布导出的，并通过有限差分方案计算。Riccati 方程的最优性通过验证论证进行分析。supOU 过程基于常年河流的实际数据进行参数化。通过计算实验分析了数值方案的收敛性。