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This monograph explores the design of controllers that suppress oscillations and instabilities in congested traffic flow using PDE backstepping methods. The first part of the text is concerned with basic backstepping control of freeway traffic using the Aw-Rascle-Zhang (ARZ) second-order PDE model. 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. Because large uncertainties may arise in traffic models, adaptive control and reinforcement learning methods are also explored in detail.
Backstepping for Coupled Hyperbolic PDEs
Basic Backstepping Control of Freeway Traffic
Stabilization of ARZ Model
Observer Validation on Freeway Data
Adaptive Control of ARZ Traffic Model
Event-Triggered Control of ARZ Model
Comparison of Backstepping with Reinforcement Learning
Advanced Backstepping for Traffic Flows
Two-Lane Traffic Control
Two-Class Traffic Control
Control of Two Cascaded Freeway Segments
Estimation of Freeway Diverge Flows
Control Under Routing-Induced Instability
Bilateral Regulation of Moving Shock Position
Extremum Seeking for Flow Maximization at Downstream Bottleneck