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On the stability of traffic perimeter control in two-region urban cities

机译：两区城市交通周界控制的稳定性

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In this paper, stability analysis of traffic control for two-region urban cities is treated. It is known in control theory that optimality does not imply stability. If the optimal control is applied in a heavily congested system with high demand, traffic conditions might not change or the network might still lead to gridlock. A city partitioned in two regions with a Macroscopic Fundamental Diagram (MFD) for each of the regions is considered. Under the assumption of triangular MFDs, the two-region MFDs system is modeled as a piecewise second-order system. Necessary and sufficient conditions are derived for stable equilibrium accumulations in the undersaturated regimes for both MFDs. Moreover, the traffic perimeter control problem for the two-region MFDs system is formulated. Phase portraits and stability analysis are conducted, and a new algorithm is proposed to derive the boundaries of the stable and unstable regions. Based on these regions, a state-feedback control strategy is derived. Trapezoidal shape of MFDs are also addressed with numerical solutions.
机译：本文对两地城市的交通控制稳定性进行了分析。在控制理论中众所周知，最优并不意味着稳定性。如果将最佳控制应用于要求很高的严重拥塞系统中，则流量条件可能不会改变，或者网络可能仍会导致僵局。考虑一个城市，该城市分为两个区域，每个区域都有宏观基本图（MFD）。在三角形MFD的假设下，将两区域MFD系统建模为分段二阶系统。推导了两个MFD在欠饱和状态下稳定平衡积累所需的充分条件。此外，提出了两区域MFD系统的交通周界控制问题。进行了相图和稳定性分析，提出了一种新的算法来导出稳定和不稳定区域的边界。基于这些区域，得出状态反馈控制策略。 MFD的梯形形状也可以通过数值解来解决。

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