Optimal Policies in a Nonlinear Bioeconomic Model of Eutrophication

摘要

The result of the paper by R. Mosetti [Optimal policies in a bioeconomic model of eutrophication, Appl. Math. Comput. 26:257-265 (1988)] is extended to the case of nonlinear growth of biomass. We have a reservoir (lake, pond, etc.) containing the biomass (for example, red algae). We estimate the environmental damage caused by this biomass as a function of concentration of biomass. The dynamics of development of biomass is described by a nonlinear equation. Control is associated with the process of eutrophication. The economic cost associated with the use of control we estimate as linear function of the control. The aim is synthesis of the control minimizing the economic cost and the environmental damage. This problem is solved with thehelp of the Pontryagin maximum principle.