A mathematical formulation for optimal control of air pollution

The problem of optimal control of air pollution using weather forecast results and numerical air pollution models is discussed. A mathematical formulation of the problem is presented. The control is an act on pollution sources with feasible constraints. Based on forecasted weather conditions, the objective of the optimal control is to minimize total cost caused by control under the constraint that the pollution concentrations over a certain period and a certain spatial domain are less than some specified values. Using the adjoint method, an effective algorithm is given. Since the optimal solutions are based on weather forecasts, the errors in weather forecasts will cause uncertainties in the optimal solutions. Estimation of impacts of weather forecast errors on the optimal solutions is discussed using the adjoint sensitivity analysis technique that is an approximated, however very effective method. The adjoint sensitivity analysis technique can be used to calculate the impacts of errors in wind, temperature and initial pollutant concentration fields on performances of the optimal control.