Modeling And Analysis Of Linear Hyperbolic Systems Of Balance Laws

This monograph focuses on the mathematical modeling of distributed parameter systems in which mass/energy transport or wave propagation phenomena occur and which are described by partial differential equations of hyperbolic type. The case of linear (or linearized) 2 x 2 hyperbolic systems of balance laws is considered, i.e., systems described by two coupled linear partial differential equations with two variables representing physical quantities, depending on both time and one-dimensional spatial variable. Based on practical examples of a double-pipe heat exchanger and a transportation pipeline, two typical configurations of boundary input signals are analyzed: collocated, wherein both signals affect the system at the same spatial point, and anti-collocated, in which the input signals are applied to the two different end points of the system. The results of this book emerge from the practical experience of the author gained during his studies conducted in the experimental installation of a heat exchange center as well as from his research experience in the field of mathematical and computer modeling of dynamic systems. The book presents valuable results concerning their state-space, transfer function and time-domain representations, which can be useful both for the open-loop analysis as well as for the closed-loop design. The book is primarily intended to help professionals as well as undergraduate and postgraduate students involved in modeling and automatic control of dynamic systems.

This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control. Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.

This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation. Such estimates shed light on why those algorithms based on source terms handled like "local scatterers" can outperform other, more standard, numerical schemes. Two-dimensional Riemann problems for the linear wave equation are also solved, with discussion of the issues raised relating to the treatment of 2D balance laws. All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements.

This volume includes four lecture courses by Bressan, Serre, Zumbrun and Williams and a Tutorial by Bressan on the Center Manifold Theorem. Bressan introduces the vanishing viscosity approach and clearly explains the building blocks of the theory. Serre focuses on existence and stability for discrete shock profiles. The lectures by Williams and Zumbrun deal with the stability of multidimensional fronts.

This book presents the proceedings of the 20th Polish Control Conference. A triennial event that was first held in 1958, the conference successfully combines its long tradition with a modern approach to shed light on problems in control engineering, automation, robotics and a wide range of applications in these disciplines. The book presents new theoretical results concerning the steering of dynamical systems, as well as industrial case studies and worked solutions to real-world problems in contemporary engineering. It particularly focuses on the modelling, identification, analysis and design of automation systems; however, it also addresses the evaluation of their performance, efficiency and reliability. Other topics include fault-tolerant control in robotics, automated manufacturing, mechatronics and industrial systems. Moreover, it discusses data processing and transfer issues, covering a variety of methodologies, including model predictive, robust and adaptive techniques, as well as algebraic and geometric methods, and fractional order calculus approaches. The book also examines essential application areas, such as transportation and autonomous intelligent vehicle systems, robotic arms, mobile manipulators, cyber-physical systems, electric drives and both surface and underwater marine vessels. Lastly, it explores biological and medical applications of the control-theory-inspired methods.

Systems of partial differential equations reflecting conservation laws hold significant relevance to a variety of theoretical and practical applications, including compressible fluid flow, electromagnetism, elasticity theory, and other areas of continuum mechanics. This field of nonlinear analysis is currently experiencing a marked increase in successful research activity. The EU-TMR network "Hyperbolic Systems of Conservation Laws held a summer program offering short courses on the Analysis of Systems of Conservation Laws. This book contains five of the self-contained short courses presented during this program by experts of international reputation. These courses, which address solutions to hyperbolic systems by the front tracking method, non-strictly hyperbolic conservation laws, hyperbolic-elliptic coupled systems, hyperbolic relaxation problems, the stability of nonlinear waves in viscous media and numerics, and more, represent the state of the art of most central aspects of the field.

This book provides a broad overview of the current problems, challenges and solutions in the field of control theory, communication theory and computational resources management. Recent results on dynamical systems, which open new opportunities for research and challenges to be addressed in the future, are proposed in the context of computational and communication constraints. In order to take into the account complex phenomena, such as nonlinearities, time-varying parameters and limited availability of information, the book proposes new approaches for open problems with both theoretical and practical significance. The contributors’ research is centred on robust stability and performance of control loops that are subject to computational and communication constraints. A particular focus is placed on the presence of constraints in communication and computation, which is a critical issue in networked control systems and cyber-physical systems. The contributions, which rely on the development of novel paradigms are provided are by leading experts in the field from all over the world, thus providing readers with the most accurate solutions for the constraints. Control subject to Computational and Communication Constraints highlights many problems encountered by control researchers, while also informing graduate students of the many interesting ideas at the frontier between control theory, information theory and computational theory. The book is also a useful point of reference for engineers and practitioners, and the survey chapters will assist instructors in lecture preparation.

This book is a tribute to Professor Laurent Praly and follows on from a workshop celebrating the occasion of his 60th birthday. It presents new and unified visions of the numerous problems that Laurent Praly has worked on in his prolific career: adaptive control, output feedback and observers, stability and stabilization. His main contributions are the central topic of this book. The book collects contributions written by prominent international experts in the control community, addressing a rich variety of topics: emerging ideas, advanced applications, and theoretical concepts. Organized in three sections, the first section covers the field of adaptive control, where Laurent Praly started his career. The second section focuses on stabilization and output feedback, which is also the topic of the second half of his career. Lastly, the third section presents the emerging research that will form Laurent Praly’s scientific legacy.