Perimeter control is an effective city-scale solution to tackle congestion problems in urban networks. To accommodate the unpredictable dynamics of congestion propagation, it is essential to incorporate real-time robustness against travel demand fluctuations into a pragmatic perimeter control strategy. This paper proposes robust perimeter control algorithms based on partial information feedback from the network. The network dynamics are modeled using the concept of the Macroscopic Fundamental Diagram (MFD), where a heterogeneously congested network is assumed to be partitioned into two homogeneously congested regions, and an outer region that acts as demand origin and destination. The desired operating condition of the network is obtained by solving an optimization program. Observer-based H_∞ proportional (P) and proportional-integral (PI) controllers are designed based on Lyapunov theory, to robustly regulate the accumulation of each region and consequently to maximize the network outflow. The controller design algorithms further accommodate operational constraints by guarantying: (i) the boundedness of the perimeter control signals and (ii) a bounded offset between the perimeter control signals. Control parameters are designed off-line by solving a set of linear matrix inequalities (LMI), which can be solved efficiently. Comprehensive numerical studies conducted on the nonlinear model of the network highlight the effectiveness of the proposed robust control algorithms in improving the congestion in the presence of time-varying disturbance in travel demand.

周边控制是解决城市网络中拥堵问题的有效的城市规模解决方案。为了适应拥塞传播的不可预测的动态，必须将针对旅行需求波动的实时鲁棒性纳入实用的周边控制策略中。本文提出了基于来自网络的部分信息反馈的鲁棒周边控制算法。使用宏观基本图（MFD）的概念对网络动力学进行建模，其中将异构拥塞的网络划分为两个均匀拥塞的区域，将外部区域用作需求的起点和目的地。通过求解优化程序可以获得网络的期望运行条件。基于观测器的H ^ _∞基于Lyapunov理论设计比例（P）和比例积分（PI）控制器，以稳健地调节每个区域的累积，从而最大程度地提高网络流出量。控制器设计算法通过保证：（i）周边控制信号的有界性和（ii）周边控制信号之间的有界偏移来进一步适应操作约束。通过解决一组线性矩阵不等式（LMI），可以离线设计控制参数，可以有效地解决这些问题。在网络的非线性模型上进行的综合数值研究突显了所提出的鲁棒控制算法在改善旅行需求时变干扰的情况下改善交通拥堵的有效性。