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

A Convex Reformulation of the Robust Freeway Network Control Problem with Controlled Merging Junctions