Traffic Congestion Control by PDE Backstepping

This monograph explores the design of controllers that suppress oscillations and instabilities in congested traffic flow using PDE backstepping methods. It begins by illustrating a basic control problem – suppressing traffic with stop-and-go oscillations downstream of ramp metering – before turning to the more challenging case for traffic upstream of ramp metering. The authors demonstrate how to design state observers for the purpose of stabilization using output-feedback control. Experimental traffic data are then used to calibrate the ARZ model and validate the boundary observer design. Adaptive control and reinforcement learning methods are also explored in detail. Part II then extends the conventional ARZ model to address more complex traffic conditions, and the final chapters demonstrate the use of the LWR first-order PDE model to regulate congestion and optimize flow through a bottleneck.

Format: Hardback
Length: 356 pages
Publication date: 18 December 2022
Publisher: Birkhauser Verlag AG

This monograph delves into the design of controllers that mitigate oscillations and instabilities in congested traffic flow through the application of PDE backstepping methods. The first part of the text focuses on fundamental backstepping control of freeway traffic employing the Aw-Rascle-Zhang (ARZ) second-order PDE model. It begins by illustrating a basic control challenge, namely suppressing traffic with stop-and-go oscillations downstream of ramp metering, before delving into the more intricate case of traffic upstream of ramp metering. The authors showcase how to design state observers for stabilization purposes through output-feedback control. Subsequently, experimental traffic data are utilized to calibrate the ARZ model and validate the boundary observer design. Given the inherent uncertainties in traffic models, adaptive control and reinforcement learning methods are explored in depth.

Part II of the monograph extends the conventional ARZ model to address more complex traffic scenarios, encompassing multi-lane traffic, multi-class traffic, networks of freeway segments, and driver utilization of routing apps. The final chapters demonstrate the application of the Lighthill-Whitham-Richards (LWR) first-order PDE model to regulate congestion in traffic flows and optimize flow through a bottleneck. To ensure self-sufficiency, an introduction to the PDE backstepping method for systems of coupled first-order hyperbolic PDEs is provided.

Traffic Congestion Control by PDE Backstepping is an invaluable resource for control theorists engaged in the control of systems modeled by PDEs, as well as traffic engineers and applied scientists working on unsteady traffic flows. It will also serve as a valuable reference for researchers interested in boundary control of coupled systems of first-order hyperbolic PDEs.

Weight: 729g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031193453
Edition number: 1st ed. 2022