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Optimization-based One-side Boundary Control of LWR Traffic Models

  • Eryn Vaid
  • Maria Teresa Chiri
  • Roberto Guglielmi
  • Gennaro Notomista
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Abstract

In this paper, we study the feasibility of a class of optimization-based boundary control of one-dimensional macroscopic traffic flow models, where stability and invariance are achieved by a single boundary control. We define the sets of controllers to stabilize the system to a desired state via Lyapunov functionals, and to ensure forward invariance of a desired subset via boundary control barrier functionals. The control input is then selected from the intersection of those sets via a convex optimization problem. We determine sufficient conditions to ensure the existence of an optimal boundary control problem achieving both stability and invariance for a generic traffic flux function. Simulation results showcase the behavior of the proposed optimization-based controller applied to conservation laws with several traffic flow functions.

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Cite

BibTeXRIS
BibTeX
@misc{vaid2026optimizationbased,
  title = {{Optimization-based One-side Boundary Control of LWR Traffic Models}},
  author = {Eryn Vaid and Maria Teresa Chiri and Roberto Guglielmi and Gennaro Notomista},
  howpublished = {arXiv},
  year = {2026},
  month = jul,
  doi = {10.48550/arxiv.2605.00004},
  eprint = {2605.00004},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.00004},
}
RIS
TY  - UNPB
TI  - Optimization-based One-side Boundary Control of LWR Traffic Models
AU  - Eryn Vaid
AU  - Maria Teresa Chiri
AU  - Roberto Guglielmi
AU  - Gennaro Notomista
PY  - 2026
DA  - 2026/07/27
PB  - arXiv
DO  - 10.48550/arxiv.2605.00004
UR  - https://arxiv.org/abs/2605.00004
AB  - In this paper, we study the feasibility of a class of optimization-based boundary control of one-dimensional macroscopic traffic flow models, where stability and invariance are achieved by a single boundary control. We define the sets of controllers to stabilize the system to a desired state via Lyapunov functionals, and to ensure forward invariance of a desired subset via boundary control barrier functionals. The control input is then selected from the intersection of those sets via a convex optimization problem. We determine sufficient conditions to ensure the existence of an optimal boundary control problem achieving both stability and invariance for a generic traffic flux function. Simulation results showcase the behavior of the proposed optimization-based controller applied to conservation laws with several traffic flow functions.
ER  -