The optimal reclamation of eutrophic water bodies

摘要

The reclamation of a eutrophic water body is set as an optimal control problem. The aim is to take account of some basic biological and economic features which were disregarded in previous analyses of the problem. To this end, an optimization model is developed where phytoplankton and nutrients are the state variables, the efficiency of the wastewater treatment system is the control variable, and minimizing the discounted stream of both environmental and treatment cost is the objective. Through a singular perturbation argument a reduced order dynamic model is obtained, to which Pontryagin's principle is applied. The optimal solution is such that (1) an optimal equilibrium for phytoplankton is achieved in the long run, and (2) both phytoplankton and the efficiency of the treatment system strictly decrease with time.