ABSTRACT
Introduction Consider a network of open channels and pipes with free surface flow as in a sewage system. The dynamic behavior of the water flow in each single channel or pipe of this system can be modeled by the de St. Venant equations, which form a system of hyperbolic conservation laws. The channels and pipes correspond to the edges of a graph, where the nodes correspond to the junctions. The flow through these points where the channels/pipes are connected is governed by a set of algebraic node conditions that guarantee for example that in the node mass is neither generated nor destroyed. At certain points in the network, the flow is controlled by devices such as pumps or underflow gates. What is the best way to operate these control devices? This question gives rise to a problem of optimal control of the type that we consider in this paper.
