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 junctions are controlled, there exist tight convex relaxations of the corresponding optimization problem. In practice, many parameters of this optimization problem are not known with certainty, in particular the fundamental diagram and predictions of future traffic demand. This uncertainty poses a challenge for 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.

在高速公路网络控制（FNC）问题中，仅使用流控制来优化交通网络的运行。对于FNC问题的特殊情况，尤其是在控制所有合并结的情况下，相应优化问题存在紧密的凸松弛。实际上，尚不确定该优化问题的许多参数，特别是基本图表和对未来交通需求的预测。这种不确定性对追求基于模型和优化策略的控制方法提出了挑战。在这项工作中，我们提出了一个与FNC问题相对应的健壮对口，在此我们为基本图和未来，外部流量需求引入了不确定性集，并寻求优化系统操作，从而将最坏情况的成本降至最低。