Traffic Congestion Control by PDE Backstepping

​Miroslav Krstic is Fellow of SIAM, IEEE, IFAC, ASME, AAAS, IET, AIAA (AF), and the Serbian Academy of Sciences and Arts. His awards include the Bellman, Reid, Oldenburger, Ragazzini, Chestnut, Paynter, Nyquist Lecture, IFAC Nonlinear Control , IFAC Ruth Curtain DPS, Balakrishnan, Axelby, and Schuck (’96 and ’19). He has served as EiC or senior editor in Systems & Control Letters, Automatica, and IEEE Transactions on Automatic Control. Four of Krstic’s 18 coauthored books have been with this Birkhäuser series, including the single-authored Delay Compensation for Nonlinear, Adaptive, and PDE Systems. 

Introduction.- Backstepping for Coupled Hyperbolic PDEs.- Part I: Basic Backstepping Control of Freeway Traffic.- Stabilization of ARZ Model with Known Parameters and Fundamental Diagram.- Observer Validation on Freeway Data.- Adaptive Control of ARZ Traffic Model.- Event-Triggered Control of ARZ Model.- Comparison of Backstepping with Reinforcement Learning.- Part II: 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 of Downstream Bottleneck.

"This book provides a mathematically rigorous framework for the control of congested traffic flow on highways in various contexts. ... Through its combination of theory, modeling of various phenomena, and the derived solutions to many important control problems, the text provides a valuable resource for researchers working in control of hyperbolic PDEs, engineers interested in traffic flow applications, and also for both instructors and readers seeking a self-contained and complete textbook on traffic congestion control." (Christophe Prieur, IEEE Control Systems Magazine, Vol. 44 (3), June, 2024)

"The book is well-organized, with excellent information, great formulas, stunning figures, and references to over 320 papers. The presentation is superb and simple to understand. It will benefit students, researchers, professors, and the general public." (P. Senthil Kumar, zbMATH 1519.90001, 2023)