Relaxation methods for hyperbolic PDE mixed-integer optimal control problems

Summary The convergence analysis for methods solving partial differential equations constrained optimal control problems containing both discrete and continuous control decisions based on relaxation and rounding strategies is extended to the class of first order semilinear hyperbolic systems in one space dimension. The results are obtained by novel a priori estimates for the size of the relaxation gap based on the characteristic flow, fixed-point arguments, and particular regularity theory for such mixed-integer control problems. Motivated by traffic flow problems, a relaxation model for optimal flux switching control in conservation laws is considered as an application.