MODELING AND CONTROL OF THE POLLUTION OF WATER RESOURCES SYSTEMS VIA MULTILEVEL APPROACH1

Abstract

ABSTRACT. The problem of modeling and control of water pollution is considered. A general mathematical model, where the pollution effluent is discharged directly into the river, into the lake, or into a bypass pipe leading to an advanced Waste Water Treatment (AWT) plant, is developed. The Water Resource System (WRS) under consideration is decomposed into N subsystems. The pollution effluent input vector to each subsystem includes the water quantity and different water characteristics such as BOD, DO, pH, conductivity, temperature, algae, phosphates, nitrates, etc. Treatment cost functions and quality transition functions as well as system model constraints are introduced, where all functions can be nonlinear. A system Lagrangian is formed to incorporate the system constraints and coupling. The Lagrangian is decomposed into N independent subsystems, and a two level optimization methodology is introduced. Each subsystem is independently and separately minimized at the first level assuming known Lagrange multipliers. At the second level, the total Lagrangian is maximized with respect to the Lagrange multipliers using optimal values for effluent inputs from all subsystems obtained from the first level. Economic interpretation on the Lagrange multipliers reveals that they are merely prices imposed by the central authority (second level) for the pollution caused by the subsystems. Advantages of the multilevel approach are discussed.