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Author: Arjan J. van der Schaft Publisher: Springer ISBN: 1846285429 Category : Technology & Engineering Languages : en Pages : 189
Book Description
This book is about dynamical systems that are "hybrid" in the sense that they contain both continuous and discrete state variables. Recently there has been increased research interest in the study of the interaction between discrete and continuous dynamics. The present volume provides a first attempt in book form to bring together concepts and methods dealing with hybrid systems from various areas, and to look at these from a unified perspective. The authors have chosen a mode of exposition that is largely based on illustrative examples rather than on the abstract theorem-proof format because the systematic study of hybrid systems is still in its infancy. The examples are taken from many different application areas, ranging from power converters to communication protocols and from chaos to mathematical finance. Subjects covered include the following: definition of hybrid systems; description formats; existence and uniqueness of solutions; special subclasses (variable-structure systems, complementarity systems); reachability and verification; stability and stabilizability; control design methods. The book will be of interest to scientists from a wide range of disciplines including: computer science, control theory, dynamical system theory, systems modeling and simulation, and operations research.
Author: Arjan J. van der Schaft Publisher: Springer ISBN: 1846285429 Category : Technology & Engineering Languages : en Pages : 189
Book Description
This book is about dynamical systems that are "hybrid" in the sense that they contain both continuous and discrete state variables. Recently there has been increased research interest in the study of the interaction between discrete and continuous dynamics. The present volume provides a first attempt in book form to bring together concepts and methods dealing with hybrid systems from various areas, and to look at these from a unified perspective. The authors have chosen a mode of exposition that is largely based on illustrative examples rather than on the abstract theorem-proof format because the systematic study of hybrid systems is still in its infancy. The examples are taken from many different application areas, ranging from power converters to communication protocols and from chaos to mathematical finance. Subjects covered include the following: definition of hybrid systems; description formats; existence and uniqueness of solutions; special subclasses (variable-structure systems, complementarity systems); reachability and verification; stability and stabilizability; control design methods. The book will be of interest to scientists from a wide range of disciplines including: computer science, control theory, dynamical system theory, systems modeling and simulation, and operations research.
Author: Len Pismen Publisher: CRC Press ISBN: 0429950144 Category : Mathematics Languages : en Pages : 360
Book Description
This book provides working tools for the study and design of nonlinear dynamical systems applicable in physics and engineering. It offers a broad-based introduction to this challenging area of study, taking an applications-oriented approach that emphasizes qualitative analysis and approximations rather than formal mathematics or simulation. The author, an internationally recognized authority in the field, makes extensive use of examples and includes executable Mathematica notebooks that may be used to generate new examples as hands-on exercises. The coverage includes discussion of mechanical models, chemical and ecological interactions, nonlinear oscillations and chaos, forcing and synchronization, spatial patterns and waves. Key Features: · Written for a broad audience, avoiding dependence on mathematical formulations in favor of qualitative, constructive treatment. · Extensive use of physical and engineering applications. · Incorporates Mathematica notebooks for simulations and hands-on self-study. · Provides a gentle but rigorous introduction to real-world nonlinear problems. · Features a final chapter dedicated to applications of dynamical systems to spatial patterns. The book is aimed at student and researchers in applied mathematics and mathematical modelling of physical and engineering problems. It teaches to see common features in systems of different origins, and to apply common methods of study without losing sight of complications and uncertainties related to their physical origin.
Author: Steven L. Brunton Publisher: Cambridge University Press ISBN: 1009098489 Category : Computers Languages : en Pages : 615
Book Description
A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
Author: Asish Ghosh Publisher: Springer ISBN: 3319107356 Category : Science Languages : en Pages : 252
Book Description
This book is a study of the interactions between different types of systems, their environment, and their subsystems. The author explains how basic systems principles are applied in engineered (mechanical, electromechanical, etc.) systems and then guides the reader to understand how the same principles can be applied to social, political, economic systems, as well as in everyday life. Readers from a variety of disciplines will benefit from the understanding of system behaviors and will be able to apply those principles in various contexts. The book includes many examples covering various types of systems. The treatment of the subject is non-mathematical, and the book considers some of the latest concepts in the systems discipline, such as agent-based systems, optimization, and discrete events and procedures.
Author: Mohamed Djemai Publisher: Springer ISBN: 331910795X Category : Technology & Engineering Languages : en Pages : 341
Book Description
This book is a collection of contributions defining the state of current knowledge and new trends in hybrid systems – systems involving both continuous dynamics and discrete events – as described by the work of several well-known groups of researchers. Hybrid Dynamical Systems presents theoretical advances in such areas as diagnosability, observability and stabilization for various classes of system. Continuous and discrete state estimation and self-triggering control of nonlinear systems are advanced. The text employs various methods, among them, high-order sliding modes, Takagi–Sugeno representation and sampled-data switching to achieve its ends. The many applications of hybrid systems from power converters to computer science are not forgotten; studies of flexible-joint robotic arms and – as representative biological systems – the behaviour of the human heart and vasculature, demonstrate the wide-ranging practical significance of control in hybrid systems. The cross-disciplinary origins of study in hybrid systems are evident. Academic researchers and graduate students interested in hybrid and switched systems need look no further than Hybrid Dynamical Systems for a single source which will bring them up to date with work in this area from around the world.
Author: Rafal Goebel Publisher: Princeton University Press ISBN: 1400842638 Category : Mathematics Languages : en Pages : 227
Book Description
Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms--algorithms that feature logic, timers, or combinations of digital and analog components. With the tools of modern mathematical analysis, Hybrid Dynamical Systems unifies and generalizes earlier developments in continuous-time and discrete-time nonlinear systems. It presents hybrid system versions of the necessary and sufficient Lyapunov conditions for asymptotic stability, invariance principles, and approximation techniques, and examines the robustness of asymptotic stability, motivated by the goal of designing robust hybrid control algorithms. This self-contained and classroom-tested book requires standard background in mathematical analysis and differential equations or nonlinear systems. It will interest graduate students in engineering as well as students and researchers in control, computer science, and mathematics.
Author: Stephen Lynch Publisher: Springer Science & Business Media ISBN: 0817645861 Category : Mathematics Languages : en Pages : 481
Book Description
This book provides an introduction to the theory of dynamical systems with the aid of the Mathematica® computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. Theorems and proofs are kept to a minimum. The first section deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems.
Author: Shlomo Sternberg Publisher: Courier Corporation ISBN: 0486477053 Category : Mathematics Languages : en Pages : 276
Book Description
A pioneer in the field of dynamical systems discusses one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials include PowerPoint slides and MATLAB exercises. 2010 edition.
Author: Oded Galor Publisher: Springer Science & Business Media ISBN: 3540367764 Category : Business & Economics Languages : en Pages : 159
Book Description
This book provides an introduction to discrete dynamical systems – a framework of analysis that is commonly used in the ?elds of biology, demography, ecology, economics, engineering, ?nance, and physics. The book characterizes the fundamental factors that govern the quantitative and qualitative trajectories of a variety of deterministic, discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for those systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors that govern the evolution of state variables in the elementary context of one-dimensional, ?rst-order, linear, autonomous systems. The f- damental insights about the forces that a?ect the evolution of these - ementary systems are subsequently generalized, and the determinants of the trajectories of multi-dimensional, nonlinear, higher-order, non- 1 autonomous dynamical systems are established. Chapter 1 focuses on the analysis of the evolution of state variables in one-dimensional, ?rst-order, autonomous systems. It introduces a method of solution for these systems, and it characterizes the traj- tory of a state variable, in relation to a steady-state equilibrium of the system, examining the local and global (asymptotic) stability of this steady-state equilibrium. The ?rst part of the chapter characterizes the factors that determine the existence, uniqueness and stability of a steady-state equilibrium in the elementary context of one-dimensional, ?rst-order, linear autonomous systems.
Author: Richard A. Holmgren Publisher: Springer Science & Business Media ISBN: 1441987320 Category : Mathematics Languages : en Pages : 231
Book Description
Given the ease with which computers can do iteration it is now possible for almost anyone to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. Mathematica programs that illustrate the dynamics are included in an appendix.
Author: Arjan J. van der Schaft
Author: Arjan J. van der Schaft
Author: Len Pismen
Author: Steven L. Brunton
Author: Asish Ghosh
Author: Mohamed Djemai
Author: Rafal Goebel
Author: Stephen Lynch
Author: Shlomo Sternberg
Author: Oded Galor
Author: Richard A. Holmgren