M. Hajiahmadi, J. Haddad, B. De Schutter, and N. Geroliminis, "Optimal hybrid macroscopic traffic control for urban regions: Perimeter and switching signal plans controllers," Proceedings of the 2013 European Control Conference, Zürich, Switzerland, pp. 3500-3505, July 2013.
The dynamics of a heterogeneous large-scale urban network is modeled as R homogeneous regions with the macroscopic fundamental diagrams (MFDs) representations. The MFD provides for homogeneous network regions a unimodal, low-scatter relationship between network vehicle density and network space-mean flow. In this paper, the optimal hybrid control problem for an R-region MFD network is formulated as a mixed integer nonlinear optimization problem, where two types of controllers are introduced: (i) perimeter controllers, and (ii) switching signal timing plans controllers. The perimeter controllers are located on the border between the regions, as they manipulate the transfer flows between them, while the switching controllers control the dynamics of the urban regions, as they define the shape of the MFDs, and as a result affect the internal flows within each region. Moreover, to decrease the computational complexity due to the nonlinear and non-convex nature of the formulated optimization problem, we re-write the problem as a mixed integer linear problem utilizing a piecewise affine approximation technique. The performance of the two problems is evaluated and compared for different traffic scenarios for a two-region urban case study.