Traffic Congestion Control by PDE Backstepping
Title | Traffic Congestion Control by PDE Backstepping PDF eBook |
Author | Huan Yu |
Publisher | Springer Nature |
Pages | 363 |
Release | 2022-12-16 |
Genre | Science |
ISBN | 3031193466 |
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. Part II then extends the conventional ARZ model utilized until this point in order to address more complex traffic conditions: multi-lane traffic, multi-class traffic, networks of freeway segments, and driver use of routing apps. The final chapters demonstrate the use of the Lighthill-Whitham-Richards (LWR) first-order PDE model to regulate congestion in traffic flows and to optimize flow through a bottleneck. In order to make the text self-contained, an introduction to the PDE backstepping method for systems of coupled first-order hyperbolic PDEs is included. Traffic Congestion Control by PDE Backstepping is ideal for control theorists working on control of systems modeled by PDEs and for traffic engineers and applied scientists working on unsteady traffic flows. It will also be a valuable resource for researchers interested in boundary control of coupled systems of first-order hyperbolic PDEs.
AI-enabled Technologies for Autonomous and Connected Vehicles
Title | AI-enabled Technologies for Autonomous and Connected Vehicles PDF eBook |
Author | Yi Lu Murphey |
Publisher | Springer Nature |
Pages | 563 |
Release | 2022-09-07 |
Genre | Technology & Engineering |
ISBN | 3031067800 |
This book reports on cutting-edge research and advances in the field of intelligent vehicle systems. It presents a broad range of AI-enabled technologies, with a focus on automated, autonomous and connected vehicle systems. It covers advanced machine learning technologies, including deep and reinforcement learning algorithms, transfer learning and learning from big data, as well as control theory applied to mobility and vehicle systems. Furthermore, it reports on cutting-edge technologies for environmental perception and vehicle-to-everything (V2X), discussing socioeconomic and environmental implications, and aspects related to human factors and energy-efficiency alike, of automated mobility. Gathering chapters written by renowned researchers and professionals, this book offers a good balance of theoretical and practical knowledge. It provides researchers, practitioners and policy makers with a comprehensive and timely guide on the field of autonomous driving technologies.
Boundary Control of Freeway Traffic Congestion
Title | Boundary Control of Freeway Traffic Congestion PDF eBook |
Author | Huan Yu |
Publisher | |
Pages | 246 |
Release | 2019 |
Genre | |
ISBN |
This dissertation develops a systematic model-based approach for the boundary control and estimation of freeway traffic congestion problem. Three topics of traffic congestion on a freeway segment are studied and include stop-and-go traffic oscillations, moving traffic shockwave, and downstream traffic bottleneck, which are governed by different partial differential equation (PDE) models and require the advancement and application of three PDE control techniques. To supress stop-and-go oscillations, we introduce the macroscopic Aw-Rascle-Zhang traffic model, consisting of second-order nonlinear hyperbolic PDEs that govern dynamics of traffic density and velocity. The hetero-directional propagations of information in congested traffic generate the instabilities, motivating us to the stabilization problem for a coupled $2\times 2$ hyperbolic system. Using the backstepping method, a full-state feedback control is designed for ramp metering at outlet to actuate the outgoing traffic flow. We design boundary observer for state estimation and combine it with the full state feedback control to construct an output feedback controller. The observer design is validated with traffic field data. Under model parameter uncertainties, adaptive control design is proposed with on-line parameter estimation. Furthermore, we develop output feedback boundary control for two types of $4\times4$ nonlinear hyperbolic PDEs which arise from two-lane and two-class traffic congestion. Stabilization of two-lane traffic involves regulation of the lane-changing interactions with lane-specific varying speed limits while stabilization of two-class traffic tackles the heterogeneity of vehicles and drivers. A moving traffic shockwave, caused by changes of local road situations, segregates light traffic upstream and heavy traffic downstream. This density discontinuity travels upstream. As a result, drivers caught in the shockwave experience transitions from free to congested traffic. The interface position is governed by an ordinary differential equation (ODE) dependent on the density of the PDE states, described with Lighthill-Whitham-Richards model. For the coupled PDE-ODE system, the predictor feedback design is applied to compensate the state-dependent input delays. We design bilateral boundary controllers to drive the moving shockwave front to a desirable setpoint position, hindering the upstream propagation of the traffic congestion. Traffic on a freeway segment with capacity drop at outlet causes a downstream bottleneck. Traffic congestion forms because the traffic at the outlet overflows its capacity. Therefore the incoming flow of the segment needs to be regulated so that the outgoing traffic at the bottleneck area is discharged with its maximum flow rate. Since the traffic dynamics of the bottleneck is hard to model, we apply extremum seeking control, a model free approach for real-time optimization, to obtain the optimal input density at the inlet. The predictor feedback design is combined with the extremum seeking to compensate the delay effect of traffic state of the segment. The maximum flow rate is achieved at the bottleneck by regulating its upstream density at the inlet.
Extremum Seeking Through Delays and PDEs
Title | Extremum Seeking Through Delays and PDEs PDF eBook |
Author | Tiago Roux Oliveira |
Publisher | SIAM |
Pages | 461 |
Release | 2022-12-05 |
Genre | Mathematics |
ISBN | 1611977355 |
Extremum Seeking through Delays and PDEs, the first book on the topic, expands the scope of applicability of the extremum seeking method, from static and finite-dimensional systems to infinite-dimensional systems. Readers will find numerous algorithms for model-free real-time optimization are developed and their convergence guaranteed, extensions from single-player optimization to noncooperative games, under delays and PDEs, are provided, the delays and PDEs are compensated in the control designs using the PDE backstepping approach, and stability is ensured using infinite-dimensional versions of averaging theory, and accessible and powerful tools for analysis. This book is intended for control engineers in all disciplines (electrical, mechanical, aerospace, chemical), mathematicians, physicists, biologists, and economists. It is appropriate for graduate students, researchers, and industrial users.
Adaptive Control of Parabolic PDEs
Title | Adaptive Control of Parabolic PDEs PDF eBook |
Author | Andrey Smyshlyaev |
Publisher | Princeton University Press |
Pages | 344 |
Release | 2010-07-01 |
Genre | Mathematics |
ISBN | 1400835364 |
This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems. Andrey Smyshlyaev and Miroslav Krstic develop explicit feedback laws that do not require real-time solution of Riccati or other algebraic operator-valued equations. The book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree. The book also presents a rich collection of methods for system identification of PDEs, methods that employ Lyapunov, passivity, observer-based, swapping-based, gradient, and least-squares tools and parameterizations, among others. Including a wealth of stimulating ideas and providing the mathematical and control-systems background needed to follow the designs and proofs, the book will be of great use to students and researchers in mathematics, engineering, and physics. It also makes a valuable supplemental text for graduate courses on distributed parameter systems and adaptive control.
Input-to-State Stability for PDEs
Title | Input-to-State Stability for PDEs PDF eBook |
Author | Iasson Karafyllis |
Publisher | Springer |
Pages | 287 |
Release | 2018-06-07 |
Genre | Technology & Engineering |
ISBN | 3319910116 |
This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes—parabolic and hyperbolic. This foundation consists of new PDE-specific tools. In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered: PDEs (of either class) with static maps; PDEs (again, of either class) with ODEs; PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and feedback loops of PDEs of different classes (parabolic with hyperbolic). In addition to stability results (including ISS), the text develops existence and uniqueness theory for all systems that are considered. Many of these results answer for the first time the existence and uniqueness problems for many problems that have dominated the PDE control literature of the last two decades, including—for PDEs that include non-local terms—backstepping control designs which result in non-local boundary conditions. Input-to-State Stability for PDEs will interest applied mathematicians and control specialists researching PDEs either as graduate students or full-time academics. It also contains a large number of applications that are at the core of many scientific disciplines and so will be of importance for researchers in physics, engineering, biology, social systems and others.
Advances in Distributed Parameter Systems
Title | Advances in Distributed Parameter Systems PDF eBook |
Author | Jean Auriol |
Publisher | Springer Nature |
Pages | 301 |
Release | 2022-04-24 |
Genre | Technology & Engineering |
ISBN | 3030947661 |
The proposed book presents recent breakthroughs for the control of distributed parameter systems and follows on from a workshop devoted to this topic. It introduces new and unified visions of the challenging control problems raised by distributed parameter systems. The book collects contributions written by prominent international experts in the control community, addressing a wide variety of topics. It spans the full range from theoretical research to practical implementation and follows three traverse axes: emerging ideas in terms of control strategies (energy shaping, prediction-based control, numerical control, input saturation), theoretical concepts for interconnected systems (with potential non-linear actuation dynamics), advanced applications (cable-operated elevators, traffic networks), and numerical aspects. Cutting-edge experts in the field contributed in this volume, making it a valuable reference source for control practitioners, graduate students, and scientists researching practical and theoretical solutions to the challenging problems raised by distributed parameter systems.