A constructive solution for optimal local control of runoff events Original Research Article

The task of optimal local control of extreme rainfall-runoff events in sewer pipe systems is outlined and formalized as a mathematical optimization problem applicable in many other similar situations. The goals of control, i.e. minimizing of overflow, uniform runoff to purification plant and effective use of retention basin, are transformed into a numerical expression with additional conditions. Along this measure the continuous inflow has to be decomposed into the three parts ongoing pipe flow, overflow and basin inflow. Whereas the existence and uniqueness of the solution can easily be realized, the derivation of a constructive and computable solution of the problem requires some preparation: For demonstration of the main theorem some auxiliary lemmas and an approximation proposition of general mathematical interest have to be proven. Some examples illustrate the calculation and application of the control functions and their effects.