Dynamics of Quasi-Stable Dissipative Systems
Title | Dynamics of Quasi-Stable Dissipative Systems PDF eBook |
Author | Igor Chueshov |
Publisher | Springer |
Pages | 405 |
Release | 2015-09-29 |
Genre | Mathematics |
ISBN | 3319229036 |
This book is devoted to background material and recently developed mathematical methods in the study of infinite-dimensional dissipative systems. The theory of such systems is motivated by the long-term goal to establish rigorous mathematical models for turbulent and chaotic phenomena. The aim here is to offer general methods and abstract results pertaining to fundamental dynamical systems properties related to dissipative long-time behavior. The book systematically presents, develops and uses the quasi-stability method while substantially extending it by including for consideration new classes of models and PDE systems arising in Continuum Mechanics. The book can be used as a textbook in dissipative dynamics at the graduate level. Igor Chueshov is a Professor of Mathematics at Karazin Kharkov National University in Kharkov, Ukraine.
Stability and Control of Large-Scale Dynamical Systems
Title | Stability and Control of Large-Scale Dynamical Systems PDF eBook |
Author | Wassim M. Haddad |
Publisher | Princeton University Press |
Pages | 389 |
Release | 2011-11-14 |
Genre | Mathematics |
ISBN | 1400842662 |
Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynamical systems are strongly interconnected and consist of interacting subsystems exchanging matter, energy, or information with the environment. The sheer size, or dimensionality, of these systems necessitates decentralized analysis and control system synthesis methods for their analysis and design. Written in a theorem-proof format with examples to illustrate new concepts, this book addresses continuous-time, discrete-time, and hybrid large-scale systems. It develops finite-time stability and finite-time decentralized stabilization, thermodynamic modeling, maximum entropy control, and energy-based decentralized control. This book will interest applied mathematicians, dynamical systems theorists, control theorists, and engineers, and anyone seeking a fundamental and comprehensive understanding of large-scale interconnected dynamical systems and control.
Dissipative Lattice Dynamical Systems
Title | Dissipative Lattice Dynamical Systems PDF eBook |
Author | Xiaoying Han |
Publisher | World Scientific |
Pages | 381 |
Release | 2023-03-14 |
Genre | Mathematics |
ISBN | 9811267774 |
There is an extensive literature in the form of papers (but no books) on lattice dynamical systems. The book focuses on dissipative lattice dynamical systems and their attractors of various forms such as autonomous, nonautonomous and random. The existence of such attractors is established by showing that the corresponding dynamical system has an appropriate kind of absorbing set and is asymptotically compact in some way.There is now a very large literature on lattice dynamical systems, especially on attractors of all kinds in such systems. We cannot hope to do justice to all of them here. Instead, we have focused on key areas of representative types of lattice systems and various types of attractors. Our selection is biased by our own interests, in particular to those dealing with biological applications. One of the important results is the approximation of Heaviside switching functions in LDS by sigmoidal functions.Nevertheless, we believe that this book will provide the reader with a solid introduction to the field, its main results and the methods that are used to obtain them.
Structures in Dynamics
Title | Structures in Dynamics PDF eBook |
Author | H.W. Broer |
Publisher | Elsevier |
Pages | 323 |
Release | 1991-11-05 |
Genre | Science |
ISBN | 0444596259 |
The study of non-linear dynamical systems nowadays is an intricate mixture of analysis, geometry, algebra and measure theory and this book takes all aspects into account. Presenting the contents of its authors' graduate courses in non-linear dynamical systems, this volume aims at researchers who wish to be acquainted with the more theoretical and fundamental subjects in non-linear dynamics and is designed to link the popular literature with research papers and monographs. All of the subjects covered in this book are extensively dealt with and presented in a pedagogic form. These include the presentation of an environment for the route to chaos by quasi-periodicity (which is related to the Landau-Lifschitz and Ruelle-Takens scenario's concerning the onset of turbulence); the theories of 1-dimensional dynamics, singularities in planar vector fields, and quasi-periodicity in dissipative systems.
Introduction to the Theory of Infinite-dimensional Dissipative Systems
Title | Introduction to the Theory of Infinite-dimensional Dissipative Systems PDF eBook |
Author | Igor' D. Čuešov |
Publisher | "Acta" publishers |
Pages | 421 |
Release | 2002 |
Genre | Differentiable dynamical systems |
ISBN | 9667021645 |
Patterns and Interfaces in Dissipative Dynamics
Title | Patterns and Interfaces in Dissipative Dynamics PDF eBook |
Author | L.M. Pismen |
Publisher | Springer Science & Business Media |
Pages | 383 |
Release | 2006-07-07 |
Genre | Science |
ISBN | 3540304312 |
Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium occurs in a variety of settings in nature and technology, and has applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology. This book explores the forefront of current research, describing in-depth the analytical methods that elucidate the complex evolution of nonlinear dissipative systems.
Dissipative Systems Analysis and Control
Title | Dissipative Systems Analysis and Control PDF eBook |
Author | Rogelio Lozano |
Publisher | Springer Science & Business Media |
Pages | 383 |
Release | 2013-03-14 |
Genre | Technology & Engineering |
ISBN | 1447136683 |
This book deals with the analysis and feedback control of dissipative dynamical systems. It presents the background of dissipative systems theory. Linear as well as nonlinear systems are treated, and many examples are given throughout the chapters. Some infinite dimensional and non-smooth examples are also included. The emphasis is put on the application towards the design of stable feedback control laws. Then the theory is illustrated on physical examples; (Lagrangian and Hamiltonian systems are thoroughly studied, as well as adaptive control). It is shown how the dissipativity properties of a system can be used in the design of stable feedback controllers. Some experimental results are presented which corroborate the theoretical developments. This monograph is primarily for readers who wish to get aquainted with Dissipative Systems Theory, and its uses in Systems and Control and Robotics. It constitutes an advanced introduction to the topic, and is the first volume ever published which is dedicated entirely to this subject.