We consider a networked system defined on a graph where each edge corresponds to a quasilinear hyperbolic system with space dimension one. At the nodes, the system is governed by algebraic node conditions. The system is controlled at the nodes of the graph. Optimal control problems for systems of this type arise in the operation of channel networks, for example in hydraulic flood routing. For the solution of such problems, the evaluation of the derivatives of functions that depend on the state of the system is necessary. For the case of continously differentiable states, we present an adjoint sensitivity calculus that allows to compute directional derivatives in seceral directions by solving only one backward equation. The result is used to numerically solve by a gradient--type method a problem of optimal control for the St. Venant Equations.
Lehrstuhl II fuer Angewandte Mathematik, Universitaet Erlangen-Nuernberg, Martensstrasse 3, 91058 Erlangen, Germany