2024/03/04 by Brian Block, Block, Brian, Stephanie Stockar +1 · 2 citations
Decision Sciences · Engineering · #FOS: Electrical engineering #Simulation Techniques and Applications #Systems and Control (eess.SY) #Traffic Prediction and Management Techniques #Traffic control and management #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2403.02507
openalex publication_date 2024/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, an extension of a linear control design for hyperbolic linear partial differential equations is presented for a first-order traffic flow model. Starting from the Lighthill-Whitham-Richards (LWR) model, variable speed limit control (VSL) is applied through a modification of Greenshield's equilibrium flow model. Then, an optimal linear quadratic (LQ) controller is designed on the linear LWR model. The LQ state feedback function is found via the solution of a Riccati differential equation. Unlike previous studies, the control input is the rate of change of the input, not the input itself. The proposed controller is then verified on both the linear and nonlinear models. In both cases, the controller is able to drive the system to a desired density profile. In the nonlinear application, a higher control gain is needed to achieve similar results as in the linear case.