On the optimal harvesting strategy for a generalized population model

We consider a harvesting problem in which the dynamics of the renewable resource is described by a generalized population model, which requires only a very basic knowledge about the evolution of the resource and the governing equations. We assume that the catch is bilinear in both the control and the stock of the resource, and solve an undiscounted infinite horizon optimal control problem, where the profit functional is assumed to be linear in the catch. We further suggest a discrete scheme that—in addition to being easily implementable—closely approximates the computed optimal control, and illustrate the effect of the proposed discrete scheme with a numerical example.