  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.
