Volume 29, 2023
|Number of page(s)||23|
|Published online||08 November 2023|
Saturated boundary feedback control of quasi-linear hyperbolic balance laws with application to LWR traffic flow stabilization
Faculty of Information Technology, Beijing University of Technology, 100124 Beijing, PR China
2 Key Laboratory of Computational Intelligence and Intelligent Systems, 100124 Beijing, PR China
* Corresponding author: email@example.com
Accepted: 25 September 2023
The saturated boundary stabilization problem for quasi-linear hyperbolic systems of balance laws is considered under H2-norm in this paper, where the boundary conditions of the system are subject to actuator saturations. The resulting closed-loop system is proven to be locally exponentially stable with respect to the steady states in the presence of saturations. To this end, the sector nonlinearity model is introduced to deal with the saturation term, and then sufficient conditions for ensuring the locally exponential stability are established in terms of a set of matrix inequalities by employing the Lyapunov function method along with a sector condition. Furthermore, these results are applied to the stabilization of the two-lane traffic flow dynamic represented by Lighthill–Whitham–Richards (LWR) model. By utilizing variable speed limit (VSL) devices, a saturated boundary feedback controller is designed to stabilize the two-lane traffic flow, and the exponential convergence of the quasi-linear traffic flow system in H2 sense is validated by numerical simulations.
Mathematics Subject Classification: 35L99 / 93D05 / 93D15 / 93D23
Key words: Quasi-linear hyperbolic systems / saturated boundary feedback control / LWR traffic flow model / Lyapunov function / sector condition
© The authors. Published by EDP Sciences, SMAI 2023
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