Traffic flow control on cascaded roads by event‐triggered output feedback
DOI: 10.1002/rnc.6122
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Summary
This paper addresses the challenge of stabilizing traffic flow on cascaded road networks to suppress stop-and-go oscillations, a common phenomenon in congested regimes that leads to increased fuel consumption and unsafe driving conditions. The authors focus on a system composed of two connected freeway segments with different intrinsic properties, modeled using the second-order Aw-Rascle-Zhang (ARZ) macroscopic partial differential equation (PDE). While previous control strategies often addressed single segments or required continuous actuation, this work proposes an event-triggered output-feedback controller that simultaneously stabilizes both upstream and downstream traffic using a single ramp metering actuator located at the outlet. This approach is motivated by the practical limitations of digital implementation, where continuous control signals are infeasible, and periodic sampling may waste computational resources or cause unnecessary actuator updates. The methodology involves linearizing the ARZ model around a congested steady state and transforming it into a coupled hyperbolic system in Riemann coordinates. The control design emulates a previously developed continuous-time backstepping boundary output feedback law, which relies on boundary measurements of flow rate and velocity at the outlet. To adapt this for digital platforms, the authors introduce a dynamic event-triggered strategy that updates the control signal only when a specific triggering condition is satisfied. The theoretical analysis employs backstepping transformations to map the closed-loop system to a simpler target system, allowing for a Lyapunov-based stability analysis. This framework is used to prove the exponential convergence of the system in the $L^2$-norm and to demonstrate the existence of a uniform minimal dwell-time, thereby avoiding the Zeno phenomenon where infinite updates would occur in finite time. The main findings confirm that the proposed event-triggered controller guarantees the simultaneous stabilization of traffic density and velocity on both cascaded road segments. The authors prove that the closed-loop system exhibits exponential convergence to the desired spatially uniform constant steady state within the congested regime. Crucially, the analysis establishes that the event-triggering mechanism ensures a minimum time interval between updates, independent of initial conditions, which prevents the Zeno phenomenon and makes the controller viable for real-world implementation. Numerical simulations are provided to illustrate the effectiveness of the control law in suppressing traffic oscillations and validating the theoretical stability results. The significance of this work lies in its contribution to the field of infinite-dimensional control systems and intelligent transportation. It represents the first attempt to design an observer-based event-triggered control law for an underactuated hyperbolic PDE system. By bridging the gap between continuous-time theoretical control designs and discrete digital implementations, the paper offers a more realistic and resource-efficient strategy for ramp metering. The avoidance of unnecessary actuation solicitations and the guarantee of stability under event-triggered updates provide a robust framework for managing complex traffic networks, enhancing both computational efficiency and traffic safety.
Key finding
The proposed event-triggered output-feedback controller guarantees exponential stabilization of traffic flow on cascaded roads while avoiding the Zeno phenomenon through a proven uniform minimal dwell-time.
Methodology
modeling
Provenance
The full processing record for this entry. Every stage of this paper's journey through the pipeline is logged — what ran, with which tool and model, how many attempts it took, and when it last completed. Discovered via author_sweep_intake on 2026-05-28.
| Stage | Outcome | Tool | Model | Prompt | Attempts | Completed |
|---|---|---|---|---|---|---|
| discover | success | author_sweep | — | — | 2 | 2026-05-28 |
| archive | success | unpaywall | — | — | 2 | 2026-06-04 |
| extract | success | cached | — | — | 3 | 2026-06-10 |
| clean | success | clean | — | — | 1 | 2026-06-04 |
| chunk | success | chunk | — | — | 1 | 2026-06-04 |
| embed | success | embed | Qwen/Qwen3-Embedding-8B | — | 1 | 2026-06-04 |
| enrich | success | — | — | — | 1 | 2026-05-28 |
| promote | success | — | — | — | 1 | 2026-06-04 |
| summarize | success | llm | qwen3.6-27b-prismaquant | summ-v5 | 2 | 2026-06-10 |
| tag | success | vector_similarity | — | — | 15 | 2026-06-11 |
| verify | success | — | — | — | 2 | 2026-06-10 |
Summary generated by qwen3.6-27b-prismaquant on 2026-06-10; verification: verified.
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