Simulation of the optimal combination of waste treatment and spatially distributed discharge of effluent using Pontryagin's minimum principle

Optimal control theory based on Pontryagin's minimum principle has been applied to the problem of specifying the best combination of minimum percent BOD waste treatment and effluent distribution policies for a single plant on a specified polluted river segment. The simulation analysis features a new dual water quality stream standard consisting of a minimum allowable dissolved oxygen concentration at every point in the river segment combined with a maximum allowable BOD concentration at a specified downstream point. The optimal BOD effluent distribution policies are compared with choice suboptimal effluent discharge patterns associated with best single point, best uniform and best bang-bang injection policies. The inequality constraints the nonlinearities in the system model, and the synthesis of the optimal controls were handled numerically in a direct manner using Pontryagin's minimum principle combined with gradient search and penalty function techniques. The results of the study very definitely established certain guidelines for increasing the assimilative capacity of a given river segment through judicious combinations of minimum percent BOD waste treatment and continuous BOD effluent distribution or dumping patterns associated with single plant effluents. The system analysis was made tractable by incorporating a no short-circuit constraint into the dumping policies.