Abstract
The boundary feedback control of networks of freeway traffic is considered in this article by means of the partial differential equation (PDE)-based techniques. The control and measurements are all located at the boundaries of each link. We have established the boundary control model for the system, a linear hyperbolic system of balance laws, which includes not only the traffic flow dynamics of the network described by combining the linearized Aw–Rascle–Zhang (ARZ) traffic flow model of each link but also the integrated on-ramping metering and variable speed limit control modeled as the boundary condition. As the traffic demand of the network is fluctuated, the boundary input-to-state stability (ISS) controller is designed to suppress the disturbance and regulate the traffic flow into the boundedness regions of the desired states. Based on a novel Lyapunov function, some sufficient conditions in terms of the matrix inequalities are derived for the ISS boundary stabilization in the <inline-formula> <tex-math notation="LaTeX">${L}^{2}$ </tex-math></inline-formula>-norm. The numerical simulation is given to illustrate the effectiveness of the developed boundary feedback control. Moreover, an interesting traffic experiment is carried out by using the traffic simulation software, AIMSUN, and some specific traffic data are collected and analyzed to verify the feasibility and effectiveness of the boundary control.
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