PI Boundary Control of Linear Hyperbolic Balance Laws with Stabilization of ARZ Traffic Flow Models

Abstract : This paper investigates the proportional-integral (PI) boundary feedback control for the linear hyperbolic systems of balance laws which control and output measures are located at the boundaries. We address the issue of feedback stabilization by means of PI boundary controllers. By constructing a new weighted Lyapunov function, the sufficient conditions in terms of matrix inequalities are developed for the exponential stability of closed-loop systems. These results are illustrated by the linearized Aw-Rascle-Zhang (ARZ) traffic flow model. We design a PI boundary controller to stabilize the oscillations of the traffic parameters of a freeway segment and evaluate the performance with numerical simulations.
Document type :
Journal articles
Complete list of metadatas

Cited literature [26 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01984388
Contributor : Christophe Prieur <>
Submitted on : Thursday, January 17, 2019 - 12:18:36 AM
Last modification on : Thursday, August 22, 2019 - 11:32:03 AM
Long-term archiving on : Thursday, April 18, 2019 - 12:46:25 PM

File

scl_july_10.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01984388, version 1

Collections

Citation

Liguo Zhang, Christophe Prieur, Junfei Qiao. PI Boundary Control of Linear Hyperbolic Balance Laws with Stabilization of ARZ Traffic Flow Models. Systems and Control Letters, Elsevier, 2019, 123, pp.85-91. ⟨hal-01984388⟩

Share

Metrics

Record views

37

Files downloads

119