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

被引：283

作者：

Haddad, Jack ^{[1
]}

Geroliminis, Nikolas ^{[1
]}

机构：

[1] Ecole Polytech Fed Lausanne, Sch Architecture Civil & Environm Engn ENAC, LUTS, CH-1015 Lausanne, Switzerland

来源：

TRANSPORTATION RESEARCH PART B-METHODOLOGICAL | 2012年 / 46卷 / 09期

关键词：

Stability characterization; Macroscopic fundamental diagram; State-feedback control; Traffic congestion; LYAPUNOV FUNCTIONS; NONLINEAR-SYSTEMS; HYBRID SYSTEMS; STABILIZATION;

D O I：

10.1016/j.trb.2012.04.004

中图分类号：

F [经济];

学科分类号：

020101 [政治经济学];

摘要：

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. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：1159 / 1176

页数：18

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