Optimization of a Class of River Aeration Problems by the Use of Multivariable Distributed Parameter Control Theory

Multivariable distributed parameter control theory has been applied to the optimization of artificial in‐stream aeration of polluted rivers. The optimization was developed for a general integral type of cost functional with weighted energy constraints. Three specific types of aeration control policies were considered: distributed space and time control, distributed time control, and distributed space control. Employing typical hydrologic coefficients with the transient version of Streeter‐Phelps equation, the optimal aeration control surfaces obtained were all found to lie well within the operating characteristics of commercial aeration equipment. Distributed parameter control theory applied to water pollution systems proved to be a powerful mathematical programing method comparable to linear and dynamic programing.