Stability And Boundary Stabilization Of 1 D Hyperbolic Systems
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| Author | : Georges Bastin |
| Publisher | : Birkhäuser |
| Total Pages | : 317 |
| Release | : 2016-07-26 |
| Genre | : Mathematics |
| ISBN | : 3319320629 |
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.
| Author | : Iasson Karafyllis |
| Publisher | : Springer |
| Total Pages | : 296 |
| 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.
| Author | : Uwe Kähler |
| Publisher | : Springer Nature |
| Total Pages | : 696 |
| Release | : 2023-12-01 |
| Genre | : Mathematics |
| ISBN | : 3031363752 |
This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.
| Author | : David Arthur Lawrenz |
| Publisher | : |
| Total Pages | : 121 |
| Release | : 1970 |
| Genre | : |
| ISBN | : |
| Author | : Sophie Tarbouriech |
| Publisher | : Springer |
| Total Pages | : 385 |
| Release | : 2018-06-01 |
| Genre | : Technology & Engineering |
| ISBN | : 3319784498 |
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.
| Author | : Alberto Bressan |
| Publisher | : Springer |
| Total Pages | : 365 |
| Release | : 2007-05-26 |
| Genre | : Mathematics |
| ISBN | : 3540721878 |
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.
| Author | : Giorgio Valmorbida |
| Publisher | : Springer Nature |
| Total Pages | : 315 |
| Release | : 2019-10-02 |
| Genre | : Science |
| ISBN | : 3030115542 |
This book contains advances on the theory and applications of time-delay systems with particular focus on interconnected systems. The methods for stability analysis and control design are based on time-domain and frequency-domain approaches, for continuous-time and sampled-data systems, linear and nonlinear systems. This volume is a valuable source of reference for control practitioners, graduate students, and scientists researching practical as well as theoretical solutions to a variety of control problems inevitably influenced by the presence of time delays. The contents are organized in three parts: Interconnected Systems analysis, Modeling and and Analysis for Delay systems, and Stabilization and Control Strategies for Delay Systems. This volume presents a selection of 19 contributions presented in the 4th DelSys Workshop which took place in Gif-sur-Yvette, France November 25-27, 2015.
| Author | : Nikolay Smirnov |
| Publisher | : Springer Nature |
| Total Pages | : 886 |
| Release | : 2022-03-15 |
| Genre | : Technology & Engineering |
| ISBN | : 3030879666 |
The proceedings of the 4th Stability and Control Processes Conference are focused on modern applied mathematics, stability theory, and control processes. The conference was held in recognition of the 90th birthday of Professor Vladimir Ivanovich Zubov (1930–2000). This selection of papers reflects the wide-ranging nature of V. I. Zubov’s work, which included contributions to the development of the qualitative theory of differential equations, the theory of rigid body motion, optimal control theory, and the theory of electromagnetic fields. It helps to advance many aspects of the theory of control systems, including questions of motion stability, nonlinear oscillations in control systems, navigation and reliability of control devices, vibration theory, and quantization of orbits. The disparate applications covered by the book – in mechanical systems, game theory, solid-state physics, socio-economic systems and medical and biological systems, control automata and navigation – are developments from Professor Zubov’s in-depth studies on the theory of stability of motion, the theory of automatic control and the theory of the motions of optimal processes. Stability and Control Processes presents research continuing the legacy of V. I. Zubov and updates it with sections focused on intelligence-based control. These proceedings will be of interest to academics, professionals working in industry and researchers alike.
| Author | : Yingmin Jia |
| Publisher | : Springer Nature |
| Total Pages | : 870 |
| Release | : 2023-11-08 |
| Genre | : Technology & Engineering |
| ISBN | : 981996847X |
This book constitutes the proceedings of the 19th Chinese Intelligent Systems Conference, CISC 2023, which was held during October 14–15, 2023, in Ningbo, Zhejiang, China. The book focuses on new theoretical results and techniques in the field of intelligent systems and control. This is achieved by providing in-depth studies of a number of important topics such as multi-agent systems, complex networks, intelligent robots, complex systems theory and swarm behavior, event-driven and data-driven control, robust and adaptive control, big data and brain science, process control, intelligent sensors and detection technology, deep learning and learning control, navigation and control of aerial vehicles, and so on. The book is particularly suitable for readers interested in learning intelligent systems and control and artificial intelligence. The book can benefit researchers, engineers and graduate students.
| Author | : Jean Auriol |
| Publisher | : Springer Nature |
| Total 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.
