A Control-Theoretic Approach for Scalable and Robust Traffic Density Estimation Using Convex Optimization
A Control-Theoretic Approach for Scalable and Robust Traffic Density Estimation Using Convex Optimization
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DOI：
10.1109/tits.2019.2953023
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发表时间：
2021-01-01
影响因子：
8.5
通讯作者：
Claudel, Christian G.
中科院分区：
文献类型：
--
作者：
Nugroho, Sebastian A.;Taha, Ahmad F.;Claudel, Christian G.
交通网络的监控和控制代表了减少交通拥堵的替代、廉价策略。由于交通传感器的数量自然受到预算要求的限制，因此实时估计未配备传感器的路段的交通流量非常重要，从而提供态势感知并指导实时反馈控制策略。为此，我们首先基于 Lighthill Whitham Richards (LWR) 流量模型建立了具有任意数量匝道流量的延伸高速公路的广义交通流模型。其次，我们表征了与 LWR 模型中存在的非线性相对应的函数集，并使用该表征为延伸的高速公路路段设计实时且鲁棒的状态估计器 (SE)。具体来说，我们通过提供解析 Lipschitz 常数来证明导出模型的非线性是局部 Lipschitz 连续的。第三，在过程和测量干扰以及未知输入的影响下，在给定有限数量的交通传感器的情况下，通过稳健的 SE 方法合并分析推导。该估计器基于凸半定优化问题的推导。最后，给出了数值测试，展示了所提出的估计器对于高强度扰动、参数不确定性和未知输入下的大型系统的适用性、可扩展性和鲁棒性。
Monitoring and control of traffic networks represent alternative, inexpensive strategies to minimize traffic congestion. As the number of traffic sensors is naturally constrained by budgetary requirements, real-time estimation of traffic flow in road segments that are not equipped with sensors is of significant importance-thereby providing situational awareness and guiding real-time feedback control strategies. To that end, firstly we build a generalized traffic flow model for stretched highways with arbitrary number of ramp flows based on the Lighthill Whitham Richards (LWR) flow model. Secondly, we characterize the function set corresponding to the nonlinearities present in the LWR model, and use this characterization to design real-time and robust state estimators (SE) for stretched highway segments. Specifically, we show that the nonlinearities from the derived models are locally Lipschitz continuous by providing the analytical Lipschitz constants. Thirdly, the analytical derivation is then incorporated through a robust SE method given a limited number of traffic sensors, under the impact of process and measurement disturbances and unknown inputs. The estimator is based on deriving a convex semidefinite optimization problem. Finally, numerical tests are given showcasing the applicability, scalability, and robustness of the proposed estimator for large systems under high magnitude disturbances, parametric uncertainty, and unknown inputs.