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：传统自然资源收获问题通常假设个体体长/体重在生理上具有同质性。然而，此类假设在现实问题中往往不成立，异质性对生物资源收获规划起着关键作用。此外，难以从现有数据直接观测到异质性。本文提出了一种新颖的最优控制框架，用于实现生物资源的经济高效收获，并应用于渔业管理。通过可偏离实际情形的概率密度函数，将异质性纳入资源动态（即种群动态）中。随后，利用散度对模型不确定性（即偏离）施加惩罚，从而形成非标准动态微分对策，其中Hamilton-Jacobi-Bellman-Isaacs (HJBI)方程包含唯一的非线性偏微分项。本文给出了HJBI方程的存在唯一性结果，并提出了显式单调有限差分方法。最后，利用实地采集数据，将所提出的最优控制应用于涉及具有休闲、经济和生态重要性的鱼类的收获问题。