Control Problems for Conservation Laws with Traffic Applications PDF Download

Author: Alexandre Bayen
Publisher: Springer Nature
ISBN: 3030930157
Category : Mathematics
Languages : en
Pages : 238

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Book Description
Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks.

Author: Alberto Bressan
Publisher: Springer Science & Business Media
ISBN: 1441995544
Category : Mathematics
Languages : en
Pages : 487

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Book Description
This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of viscous shock waves, singular limits for viscous systems, basic principles in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models of nonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In addition, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids, granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks.

Author: Günter Leugering
Publisher: Springer
ISBN: 3319050834
Category : Mathematics
Languages : en
Pages : 539

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Book Description
Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored as part of the Deutsche Forschungsgemeinschaft (DFG) priority program 1253 on “Optimization with Partial Differential Equations” from 2006 to 2013. The investigations were motivated by the fascinating potential applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume, contributions from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics. The book is divided into five sections on “Constrained Optimization, Identification and Control”, “Shape and Topology Optimization”, “Adaptivity and Model Reduction”, “Discretization: Concepts and Analysis” and “Applications”. Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview of topics that set sustainable trends for future research. This makes this special volume interesting not only for mathematicians, but also for engineers and for natural and medical scientists working on processes that can be modeled by PDEs.

Author: Antonella Ferrara
Publisher: Springer
ISBN: 3319759612
Category : Technology & Engineering
Languages : en
Pages : 324

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Book Description
This monograph provides an extended overview of modelling and control approaches for freeway traffic systems, moving from the early methods to the most recent scientific results and field implementations. The concepts of green traffic systems and smart mobility are addressed in the book, since a modern freeway traffic management system should be designed to be sustainable. Future perspectives on freeway traffic control are also analysed and discussed with reference to the most recent technological advancements The most widespread modelling and control techniques for freeway traffic systems are treated with mathematical rigour, but also discussed with reference to their performance assessment and to the expected impact of their practical usage in real traffic systems. In order to make the book accessible to readers of different backgrounds, some fundamental aspects of traffic theory as well as some basic control concepts, useful for better understanding the addressed topics, are provided in the book. This monograph can be used as a textbook for courses on transport engineering, traffic management and control. It is also addressed to experts working in traffic monitoring and control areas and to researchers, technicians and practitioners of both transportation and control engineering. The authors’ systematic vision of traffic modelling and control methods developed over decades makes the book a valuable survey resource for freeway traffic managers, freeway stakeholders and transportation public authorities with professional interests in freeway traffic systems. Advances in Industrial Control reports and encourages the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.

Author: Huan Yu
Publisher: Springer Nature
ISBN: 3031193466
Category : Science
Languages : en
Pages : 363

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Book Description
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.

Author: Emmanuel Trélat
Publisher: Elsevier
ISBN: 0323858260
Category : Mathematics
Languages : en
Pages : 662

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Book Description
Numerical Control: Part B, Volume 24 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Control problems in the coefficients and the domain for linear elliptic equations, Computational approaches for extremal geometric eigenvalue problems, Non-overlapping domain decomposition in space and time for PDE-constrained optimal control problems on networks, Feedback Control of Time-dependent Nonlinear PDEs with Applications in Fluid Dynamics, Stabilization of the Navier-Stokes equations - Theoretical and numerical aspects, Reconstruction algorithms based on Carleman estimates, and more. Other sections cover Discrete time formulations as time discretization strategies in data assimilation, Back and forth iterations/Time reversal methods, Unbalanced Optimal Transport: from Theory to Numerics, An ADMM Approach to the Exact and Approximate Controllability of Parabolic Equations, Nonlocal balance laws -- an overview over recent results, Numerics and control of conservation laws, Numerical approaches for simulation and control of superconducting quantum circuits, and much more. - Provides the authority and expertise of leading contributors from an international board of authors - Presents the latest release in the Handbook of Numerical Analysis series - Updated release includes the latest information on Numerical Control

Author: Pushkin Kachroo
Publisher: Springer
ISBN: 3319692313
Category : Technology & Engineering
Languages : en
Pages : 291

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Book Description
This book develops a methodology for designing feedback control laws for dynamic traffic assignment (DTA) exploiting the introduction of new sensing and information-dissemination technologies to facilitate the introduction of real-time traffic management in intelligent transportation systems. Three methods of modeling the traffic system are discussed: partial differential equations representing a distributed-parameter setting; continuous-time ordinary differential equations (ODEs) representing a continuous-time lumped-parameter setting; and discreet-time ODEs representing a discrete-time lumped-parameter setting. Feedback control formulations for reaching road-user-equilibrium are presented for each setting and advantages and disadvantage of using each are addressed. The closed-loop methods described are proposed expressly to avoid the counter-productive shifting of bottlenecks from one route to another because of driver over-reaction to routing information. The second edition of Feedback Control Theory for Dynamic Traffic Assignment has been thoroughly updated with completely new chapters: a review of the DTA problem and emphasizing real-time-feedback-based problems; an up-to-date presentation of pertinent traffic-flow theory; and a treatment of the mathematical solution to the traffic dynamics. Techinques accounting for the importance of entropy are further new inclusions at various points in the text. Researchers working in traffic control will find the theoretical material presented a sound basis for further research; the continual reference to applications will help professionals working in highway administration and engineering with the increasingly important task of maintaining and smoothing traffic flow; the extensive use of end-of-chapter exercises will help the graduate student and those new to the field to extend their knowledge.

Author: Mauro Garavello
Publisher: Debolsillo
ISBN: 9781601330000
Category : Conservation laws (Mathematics)
Languages : en
Pages : 0

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Book Description

Author: Satish V. Ukkusuri
Publisher: Springer Science & Business Media
ISBN: 1461462436
Category : Business & Economics
Languages : en
Pages : 322

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Book Description
This edited book focuses on recent developments in Dynamic Network Modeling, including aspects of route guidance and traffic control as they relate to transportation systems and other complex infrastructure networks. Dynamic Network Modeling is generally understood to be the mathematical modeling of time-varying vehicular flows on networks in a fashion that is consistent with established traffic flow theory and travel demand theory. Dynamic Network Modeling as a field has grown over the last thirty years, with contributions from various scholars all over the field. The basic problem which many scholars in this area have focused on is related to the analysis and prediction of traffic flows satisfying notions of equilibrium when flows are changing over time. In addition, recent research has also focused on integrating dynamic equilibrium with traffic control and other mechanism designs such as congestion pricing and network design. Recently, advances in sensor deployment, availability of GPS-enabled vehicular data and social media data have rapidly contributed to better understanding and estimating the traffic network states and have contributed to new research problems which advance previous models in dynamic modeling. A recent National Science Foundation workshop on “Dynamic Route Guidance and Traffic Control” was organized in June 2010 at Rutgers University by Prof. Kaan Ozbay, Prof. Satish Ukkusuri , Prof. Hani Nassif, and Professor Pushkin Kachroo. This workshop brought together experts in this area from universities, industry and federal/state agencies to present recent findings in this area. Various topics were presented at the workshop including dynamic traffic assignment, traffic flow modeling, network control, complex systems, mobile sensor deployment, intelligent traffic systems and data collection issues. This book is motivated by the research presented at this workshop and the discussions that followed.

Author: Iasson Karafyllis
Publisher: Springer
ISBN: 3319910116
Category : Technology & Engineering
Languages : en
Pages : 296

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Book Description
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.