Hamilton-Jacobi-Bellman-Isaacs equation for rational inattention in the long-run management of river environments under uncertainty
Hamilton-Jacobi-Bellman-Isaacs equation for rational inattention in the long-run management of river environments under uncertainty
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DOI：
10.1016/j.camwa.2022.02.013
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发表时间：
2021-07
期刊：
影响因子：
--
通讯作者：
H. Yoshioka;M. Tsujimura
中科院分区：
文献类型：
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作者：
H. Yoshioka;M. Tsujimura
针对具有独特非光滑和非线性特性的现代泥沙补给问题，对河流长期环境管理的一种新的随机控制模型进行了数学和数值分析。理性疏忽作为一种新的自适应策略，收集信息和干预对目标系统建模使用Erlangization。系统动力学包含河流流量以下的连续状态分支与移民型的过程和控制泥沙存储动态导致一个非光滑和非局部的无穷小生成器。建模的不确定性，这是无处不在的，在某些应用中，被认为是在一个强大的控制框架，其中基准和扭曲的模型之间的偏差通过相对熵惩罚。导出了作为最优性方程的偏积分微分Hamilton-Jacobi-Bellman-Isaacs（HJBI）方程，并讨论了它的唯一性、存在性和最优性.提出了一种保证数值解有界唯一性的单调差分格式离散HJBI方程，并基于人工解进行了验证。模型的应用也进行了参数值确定从现有的数据和物理公式。计算结果表明，环境管理应该是理性的疏忽状态依赖和适应性的方式。
A new stochastic control model for the long-run environmental management of rivers is mathematically and numerically analyzed, focusing on a modern sediment replenishment problem with unique nonsmooth and nonlinear properties. Rational inattention as a novel adaptive strategy to collect information and intervene against the target system is modeled using Erlangization. The system dynamics containing the river discharge following a continuous-state branching with an immigration-type process and the controlled sediment storage dynamics lead to a nonsmooth and nonlocal infinitesimal generator. Modeling uncertainty, which is ubiquitous in certain applications, is considered in a robust control framework in which deviations between the benchmark and distorted models are penalized through relative entropy. The partial integro-differential Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation as an optimality equation is derived, and its uniqueness, existence, and optimality are discussed. A monotone finite difference scheme guaranteeing the boundedness and uniqueness of numerical solutions is proposed to discretize the HJBI equation and is verified based on manufactured solutions. Model applications are also conducted with the parameter values identified from the available data and physical formulae. The computational results suggest that environmental management should be rationally inattentive in a state-dependent and adaptive manner.