Conventional harvesting problems for natural resources often assume physiological homogeneity of the body length/weight among individuals. However, such assumptions generally are not valid in real-world problems, where heterogeneity plays an essential role in the planning of biological resource harvesting. Furthermore, it is difficult to observe heterogeneity directly from the available data. This paper presents a novel optimal control framework for the cost-efficient harvesting of biological resources for application in fisheries management. The heterogeneity is incorporated into the resource dynamics, which is the population dynamics in this case, through a probability density that can be distorted from the reality. Subsequently, the distortion, which is the model uncertainty, is penalized through a divergence, leading to a non-standard dynamic differential game wherein the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation has a unique nonlinear partial differential term. Here, the existence and uniqueness results of the HJBI equation are presented along with an explicit monotone finite difference method. Finally, the proposed optimal control is applied to a harvesting problem with recreationally, economically, and ecologically important fish species using collected field data.

翻译：传统自然资源捕捞问题通常假设个体体长/体重具有生理同质性。然而，这类假设在现实问题中往往不成立，因为异质性在生物资源捕捞规划中扮演着关键角色。此外，直接通过现有数据观察异质性存在困难。本文提出一种新的最优控制框架，用于渔业管理中生物资源的成本效益型捕捞。通过一个可能偏离现实的概率密度函数，将异质性纳入资源动态（在此即种群动态）中。随后，通过散度对模型不确定性下的偏差进行惩罚，形成一种非标准动态微分博弈，其中Hamilton-Jacobi-Bellman-Isaacs（HJBI）方程包含一个独特的非线性偏微分项。本文给出了该HJBI方程解的存在唯一性结果，并提出了显式单调有限差分方法。最后，利用实地采集的具有休闲、经济和生态重要性的鱼类物种数据，将所提出的最优控制应用于实际捕捞问题。