Discontinuous Systems
Download Discontinuous Systems full books in PDF, epub, and Kindle. Read online free Discontinuous Systems ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : Yury V. Orlov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 333 |
| Release | : 2008-10-28 |
| Genre | : Technology & Engineering |
| ISBN | : 1848009844 |
Discontinuous Systems develops nonsmooth stability analysis and discontinuous control synthesis based on novel modeling of discontinuous dynamic systems, operating under uncertain conditions. While being primarily a research monograph devoted to the theory of discontinuous dynamic systems, no background in discontinuous systems is required; such systems are introduced in the book at the appropriate conceptual level. Being developed for discontinuous systems, the theory is successfully applied to their subclasses – variable-structure and impulsive systems – as well as to finite- and infinite-dimensional systems such as distributed-parameter and time-delay systems. The presentation concentrates on algorithms rather than on technical implementation although theoretical results are illustrated by electromechanical applications. These specific applications complete the book and, together with the introductory theoretical constituents bring some elements of the tutorial to the text.
| Author | : Marat Akhmet |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 185 |
| Release | : 2010-08-26 |
| Genre | : Mathematics |
| ISBN | : 1441965815 |
Discontinuous dynamical systems have played an important role in both theory and applications during the last several decades. This is still an area of active research and techniques to make the applications more effective are an ongoing topic of interest. Principles of Discontinuous Dynamical Systems is devoted to the theory of differential equations with variable moments of impulses. It introduces a new strategy of implementing an equivalence to systems whose solutions have prescribed moments of impulses and utilizing special topologies in spaces of piecewise continuous functions. The achievements obtained on the basis of this approach are described in this book. The text progresses systematically, by covering preliminaries in the first four chapters. This is followed by more complex material and special topics such as Hopf bifurcation, Devaney's chaos, and the shadowing property are discussed in the last two chapters. This book is suitable for researchers and graduate students in mathematics and also in diverse areas such as biology, computer science, and engineering who deal with real world problems.
| Author | : A.F. Filippov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 315 |
| Release | : 2013-11-22 |
| Genre | : Mathematics |
| ISBN | : 9401577935 |
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
| Author | : Vladimir Andreevich I?A?kubovich |
| Publisher | : World Scientific |
| Total Pages | : 351 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9812387196 |
This book presents a development of the frequency-domain approach to the stability study of stationary sets of systems with discontinuous nonlinearities. The treatment is based on the theory of differential inclusions and the second Lyapunov method. Various versions of the Kalman-Yakubovich lemma on solvability of matrix inequalities are presented and discussed in detail. It is shown how the tools developed can be applied to stability investigations of relay control systems, gyroscopic systems, mechanical systems with a Coulomb friction, nonlinear electrical circuits, cellular neural networks, phase-locked loops, and synchronous machines.
| Author | : Craig R. Allen |
| Publisher | : Columbia University Press |
| Total Pages | : 287 |
| Release | : 2008-07-01 |
| Genre | : Science |
| ISBN | : 0231516827 |
Following the publication of C. S. Holling's seminal work on the relationship between animal body mass patterns and scale-specific landscape structure, ecologists began to explore the theoretical and applied consequences of discontinuities in ecosystems and other complex systems. Are ecosystems and their components continuously distributed and do they adhere to scaling laws, or are they discontinuous and more complex than early models would have us believe? The resulting propositions over the structure of complex systems sparked an ongoing debate regarding the mechanisms generating discontinuities and the statistical methods used for their detection. This volume takes the view that ecosystems and other complex systems are inherently discontinuous and that such fields as ecology, economics, and urban studies greatly benefit from this paradigm shift. Contributors present evidence of the ubiquity of discontinuous distributions in ecological and social systems and how their analysis provides insight into complex phenomena. The book is divided into three sections. The first focuses on background material and contrasting views concerning the discontinuous organization of complex systems. The second discusses discontinuous patterns detected in a number of different systems and methods for detecting them, and the third touches on the potential significance of discontinuities in complex systems. Science is still dominated by a focus on power laws, but the contributors to this volume are convinced power laws often mask the interesting dynamics of systems and that those dynamics are best revealed by investigating deviations from assumed power law distributions. In 2008, a grand conference on resilience was held in Stockholm, hosting 600 participants from around the world. There are now three big centers established with resilience, the most recent one being the Stockholm Resilience Center, with others in Australia (an international coral reef center), Arizona State University's new sustainability center focusing on anthropology, and Canada's emerging social sciences and resilience center. Activity continues to flourish in Alaska, South Africa, and the Untied Kingdom, and a new center is forming in Uruguay.
| Author | : |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 516 |
| Release | : 2008 |
| Genre | : Differentiable dynamical systems |
| ISBN | : 0817644865 |
In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. The book covers the following four general topics: * Representation and modeling of dynamical systems of the types described above * Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces * Specialization of this stability theory to finite-dimensional dynamical systems * Specialization of this stability theory to infinite-dimensional dynamical systems Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.
| Author | : Daniele Antonio Di Pietro |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 392 |
| Release | : 2011-11-03 |
| Genre | : Mathematics |
| ISBN | : 3642229808 |
This book introduces the basic ideas to build discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. The presentation is to a large extent self-contained and is intended for graduate students and researchers in numerical analysis. The material covers a wide range of model problems, both steady and unsteady, elaborating from advection-reaction and diffusion problems up to the Navier-Stokes equations and Friedrichs' systems. Both finite element and finite volume viewpoints are exploited to convey the main ideas underlying the design of the approximation. The analysis is presented in a rigorous mathematical setting where discrete counterparts of the key properties of the continuous problem are identified. The framework encompasses fairly general meshes regarding element shapes and hanging nodes. Salient implementation issues are also addressed.
| Author | : Jan S. Hesthaven |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 507 |
| Release | : 2007-12-18 |
| Genre | : Mathematics |
| ISBN | : 0387720650 |
This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE’s, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE’s: Maxwell’s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.
| Author | : Viktor Avrutin |
| Publisher | : World Scientific |
| Total Pages | : 649 |
| Release | : 2019-05-28 |
| Genre | : Mathematics |
| ISBN | : 9811204713 |
The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.
| Author | : Mario Bernardo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 497 |
| Release | : 2008-01-01 |
| Genre | : Mathematics |
| ISBN | : 1846287081 |
This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.
