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/体重在生理上是同质的。然而，这类假设在现实问题中通常不成立，其中异质性在生物资源收获规划中起着关键作用。此外，直接从可用数据中观察异质性存在困难。本文提出了一种新颖的最优控制框架，用于生物资源的成本效益型收获，并应用于渔业管理。异质性通过可偏离现实情况的概率密度被纳入资源动态（即本例的种群动态）中。随后，该偏差（即模型不确定性）通过散度进行惩罚，形成了一种非标准动态微分博弈，其中Hamilton-Jacobi-Bellman-Isaacs (HJBI)方程具有唯一的非线性偏微分项。文中给出了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，利用野外实地数据，将所提出的最优控制应用于具有休闲、经济和生态重要性的鱼种收获问题。