Boundary Feedback Stabilization of Freeway Traffic Networks: ISS Control and Experiments

Abstract

Boundary feedback control of networks of freeway traffic is considered in this paper by means of Partial Differential Equations (PDEs) 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 Inputto-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 L 2 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.

Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions

“…It also includes nuclear fusion control, as studied in Bribiesca Argomedo et al (2014). More specifically, the following model for the dynamics of the safety factor profile x in a tokamak is derived in Bribiesca Argomedo et al (2014), Thus numerical methods are obtained for the design of boundary controllers of traffic flow in a network, as done for experiments on the Fourth-Ring road of Beijing, China (see Zhang et al (2021)).…”

“…11.5). See also Zhang et al (2021) where the Aw-Rascle-Zhang model for the macroscopic traffic flow dynamics is recalled, which reads for all (r, t) ∈ [0, L] × R + as…”

Traffic flow control on cascaded roads by event‐triggered output feedback

“…In Reference 10, the authors design a control law that depends on measurements of a portion of the system state and that is integrated in a LWR model. In Reference 12 or 13, the authors design PI boundary control of a cascaded freeway network, which is modeled by the linearized homogeneous AR model. The static errors of boundary conditions are suppressed since the instabilities do not arise from the transport PDEs.…”

“…The static errors of boundary conditions are suppressed since the instabilities do not arise from the transport PDEs. The proposed controllers have been tested against traffic experiment in Reference 13 that suggests that the proposed strategy is feasible and effective. The present paper differs in focusing on the oscillations generated by the in‐domain traffic that can only be modeled by the inhomogeneous ARZ model.…”

“…The present paper differs in focusing on the oscillations generated by the in‐domain traffic that can only be modeled by the inhomogeneous ARZ model. Moreover, all the boundaries of the network are actuated in References 12,13 which is not the case in this work, where we only consider that one boundary of the network is actuated. In Reference 14, the authors have proposed a control algorithm based on time‐gap setting of ACC equipped and connected vehicles in‐domain actuation.…”