Boundary Control for Multi-Directional Traffic on Urban Networks

This paper is devoted to boundary control design for urban traffic described on a macroscopic scale. The state corresponds to vehicle density that evolves on a continuum two-dimensional domain that represents a continuous approximation of a urban network. Its parameters are interpolated as a function of distance to physical roads. The dynamics are governed by a new macroscopic multi-directional traffic model that encompasses a system of four coupled partial differential equations (PDE) each describing density evolution in one direction layer: North, East, West and South (NEWS). We analyse the class of desired states that the density governed by NEWS model can achieve. Then a boundary control is designed to drive congested traffic to an equilibrium with the minimal congestion level. The result is validated numerically using the real structure of Grenoble downtown (a city in France).