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arXiv · 2605.00004

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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Eryn Vaid, Maria Teresa Chiri, Roberto Guglielmi, Gennaro Notomista. 2026-07-27. Optimization-based One-side Boundary Control of LWR Traffic Models. https://arxiv.org/abs/2605.00004

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