论文标题
用于河流环境和生态的随机控制的数学和计算方法：从渔业角度来看
Mathematical and computational approaches for stochastic control of river environment and ecology: from fisheries viewpoint
论文作者
论文摘要
我们提出了一个现代的随机控制框架，用于动态优化河流环境和生态学。我们关注日本的渔业问题，并显示了模拟渔业资源动态，水库水平动力学，底栖藻类动力学和沉积物存储动态的随机微分方程的简化最佳控制问题的几个示例。这些问题涉及彼此不同的现象，但它们都降低为解决退化的抛物线或椭圆方程。这些问题的最佳控制和价值功能是使用有限差异方案计算的。最后，我们提出了一个高维的问题，即使用稀疏网格上的半拉格朗日离散化控制大坝 - 库库系统。我们的贡献表明了环境工程和科学以及相关研究领域的随机控制的建模，分析和计算的最先进。
We present a modern stochastic control framework for dynamic optimization of river environment and ecology. We focus on a fisheries problem in Japan, and show several examples of simplified optimal control problems of stochastic differential equations modeling fishery resource dynamics, reservoir water balance dynamics, benthic algae dynamics, and sediment storage dynamics. These problems concern different phenomena with each other, but they all reduce to solving degenerate parabolic or elliptic equations. Optimal controls and value functions of these problems are computed using finite difference schemes. Finally, we present a higher-dimensional problem of controlling a dam-reservoir system using a semi-Lagrangian discretization on sparse grids. Our contribution shows the state-of-art of modeling, analysis, and computation of stochastic control in environmental engineering and science, and related research areas.
