PI boundary control of linear hyperbolic balance laws with stabilization of ARZ traffic flow models

Zhang, Liguo; Prieur, Christophe; Qiao, Junfei

doi:10.1016/j.sysconle.2018.11.005

Cited by 60 publications

(37 citation statements)

References 25 publications

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“…In order to design a boundary control law for the linearized ARZ traffic flow model, spectral analysis is applied in Reference 11. Zhang and Prieur 12 prove the local stability of a positive hyperbolic system and Zhang et al 13 design a proportional-integral (PI) boundary feedback controller to stabilize the oscillations of the traffic parameters on a freeway by Lyapunov method. Blandin et al 14 present explicit boundary conditions which guarantee the Lyapunov stability of the weak entropy solution to the scalar conservation law with convex flux.…”

Section: Introductionmentioning

confidence: 99%

Optimal observer‐based output feedback controller for traffic congestion with bottleneck

Guan

Zhang

Prieur

2021

Intl J Robust & Nonlinear

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This article designs an optimal observer-based output feedback control for traffic breakdown to dissolve traffic congestion using the backstepping method and optimization. The linearized Aw-Rascle-Zhang model is used to represent the congested traffic dynamics resulting from traffic breakdown. Based on the factors leading to traffic breakdown, we take into account the boundary conditions consisting of a boundary with a constant density and a speed drop at the upstream inlet of a bottleneck, and a boundary with a disturbance of inflow (high traffic demand) at the inlet of the road segment under consideration. To dissolve traffic congestion, a dynamic feedback controller is designed at the upstream boundary. By using the backstepping approach, an observer-based output feedback controller is computed to guarantee the integral input-to-state stability of the closed-loop system. By establishing an optimization problem and solving it, the optimal value of the considered class controller is obtained. The performance of the output feedback controller is also validated by numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Optimal observer‐based output feedback controller for traffic congestion with bottleneck

Guan

Zhang

Prieur

2021

Intl J Robust & Nonlinear

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“…A really well known example of the internal model approach is the integral action controller for tracking or rejection of constant signals, see, e.g. [3], [6], [24], [27]. For more sophisticated exosystems represented, for instance, by the combination of a finite number of linear oscillators, there exist some results devoted to abstract systems, i.e., systems described by operators, see, for instance, [17], [18].…”

Section: Introductionmentioning

confidence: 99%

Forwarding-Lyapunov design for the stabilization of coupled ODEs and exponentially stable PDEs

Marx,

Astolfi,

Andrieu

2021

Preprint

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This paper is about the stabilization of a cascade system composed by an infinite-dimensional system, that we suppose to be exponentially stable, and an ordinary differential equation (ODE), that we suppose to be marginally stable. The system is controlled through the infinite-dimensional system. Such a structure is particularly useful when applying the internal model approach on infinite-dimensional systems. Our strategy relies on the forwarding method, which uses a Lyapunov functional and a Sylvester equation to build a feedback-law. Under some classical assumptions in the output regulation theory, we prove that the closed-loop system is globally exponentially stable.

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“…We adopt a system-theoretic perspective, where v is an input. When the velocity profile is given, the continuity equation falls within the framework of transport PDEs, which are studied heavily in the literature (see for instance [2,3,4,10,11,12,14,17,18,19,21,22,24,25,29]). In this framework, the continuity equation is a bilinear transport PDE.…”

Section: Introductionmentioning

confidence: 99%

Stability results for the continuity equation

Karafyllis

Krstić

2020

Systems & Control Letters

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We provide a thorough study of stability of the 1-D continuity equation, which models many physical conservation laws. In our system-theoretic perspective, the velocity is considered to be an input. An additional input appears in the boundary condition (boundary disturbance). Stability estimates are provided in all p L state norms with 1 p  , including the case p   . However, in our Input-to-State Stability estimates, the gain and overshoot coefficients depend on the velocity. Moreover, the logarithmic norm of the state appears instead of the usual norm. The obtained results can be used in the stability analysis of larger models that contain the continuity equation. In particular, it is shown that the obtained results can be used in a straightforward way for the stability analysis of non-local, nonlinear manufacturing models under feedback control.

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PI boundary control of linear hyperbolic balance laws with stabilization of ARZ traffic flow models

Cited by 60 publications

References 25 publications

Optimal observer‐based output feedback controller for traffic congestion with bottleneck

Optimal observer‐based output feedback controller for traffic congestion with bottleneck

Forwarding-Lyapunov design for the stabilization of coupled ODEs and exponentially stable PDEs

Stability results for the continuity equation

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