A Discrete Dynamic Model with Distributed Transport Delays and Its Hierarchical Optimization for Preserving Stream Quality

A discrete dynamic model of multidimensional high-order difference equations is described for the dynamics of biochemical oxygen demand (BOD) and dissolved oxygen (DO) in a multiple-reach river system. The high-order difference equations represent the distributed transport delays between the adjacent reaches in the river to allow for the effects of dispersion of BOD and DO. A hierarchical optimization technique, which is based on duality and decomposition, is applied to the high-order discrete dynamic model having state and control constraints for minimizing the deviation of water quality from the desired level. It is shown that the distributed delay model is the most realistic one by comparing the responses for no delay, pure delay, and distributed delay models. By solving a 4-reach problem it is also shown that the hierarchical optimization technique is a powerful tool for optimizing fairly large dimensional discrete dynamic systems having distributed transport delays and state and control constraints.