Abstract

We propose a general framework to analyze control problems for conservation law models on a network where we regard as controls the boundary data on the incoming edges of a junction and the distributional parameters at the junction. Such controls yield, in general, different solutions from those obtained by the standard well-posedness theory based on the definition of suitable junction-Riemann solvers. Compactness results for classes of junction distribution and inflow controls are established. We then show the existence of optimal solutions, within classes of such controls, for several optimization problems in traffic flow models related to different traffic performance indexes considered in the literature. A variational formulation of such optimization problems is also provided and some characterization of optimal solutions is discussed.

This is a joint work with A. Cesaroni, G. M. Coclite and M. Garavello.