  In the freeway network control (FNC) problem, the operation of a traffic
network is optimized using only flow control. For special cases of the FNC
problem, in particular the case when all merging flows are controlled, there
exist tight convex relaxations of the corresponding optimization problem.
However, model uncertainty, in particular regarding the fundamental diagram and
predictions of future traffic demand, can be a problem in practice. This
uncertainty poses a challenge to control approaches that pursue a model- and
optimization-based strategy. In this work, we propose a robust counterpart to
the FNC problem, where we introduce uncertainty sets for both the fundamental
diagram and future, external traffic demands and seek to optimize the system
operation, minimizing the worst-case cost. For a network with controlled
merging junctions, and assuming that certain technical conditions on the
uncertainty sets are satisfied, we show that the robust counterpart of the FNC
problem can be reduced to a convex, finite-dimensional and deterministic
optimization problem, whose numerical solution is tractable.
