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...

This monograph explores the synchronization of large-scale, multi-agent dynamical systems in the presence of disturbances, delays, and time-varying networks.  Drawing upon their extensive work in this area, the authors provide a thorough treatment of agents with higher-order dynamics, different classes of models for agents, and the underlying networks representing the agents’ actions.  The high technical level of their presentation and their rigorous mathematical approach make this a timely and valuable resource that will fill a gap in the existing literature.Divided into two sections,...