TY - JOUR A1 - Pfaff, Sebastian A1 - Ulbrich, Stefan T1 - Optimal Control of Nonlinear Hyperbolic Conservation Laws by On/Off-Switching JF - Optimization Methods and Software N2 - This paper studies the differentiability properties of the control-to-state mapping for entropy solutions to a scalar hyperbolic conservation law on R with respect to the switching times of an on/off-control. The switching times between on-modes and off-modes are the control variables of the considered optimization problem, where a general tracking-type functional is minimized.We investigate the differentiability of the reduced objective function, also in the presence of shocks. We show that the state y(t,ยท) at some observation time t depends differentiably on the switching times in a generalized sense that implies total differentiability for the composition with a tracking functional. Furthermore, we present an adjoint-based formula for the gradient of the reduced objective functional with respect to the switching times. KW - optimal control, scalar conservation law, network Y1 - 2017 U6 - https://doi.org/10.1080/10556788.2016.1236796 VL - 32 SP - 904 EP - 939 ER -