An Introduction to Hybrid Dynamical Systems

An Introduction to Hybrid Dynamical Systems
Author: Arjan J. van der Schaft
Publisher: Springer
Total Pages: 189
Release: 2007-10-03
Genre: Technology & Engineering
ISBN: 1846285429
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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.

Asymptotic and Stationary Preserving Schemes for Kinetic and Hyperbolic Partial Differential Equations

Asymptotic and Stationary Preserving Schemes for Kinetic and Hyperbolic Partial Differential Equations
Author: Farah Kanbar
Publisher: BoD – Books on Demand
Total Pages: 154
Release: 2023-05-09
Genre: Mathematics
ISBN: 3958262104
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In this thesis, we are interested in numerically preserving stationary solutions of balance laws. We start by developing finite volume well-balanced schemes for the system of Euler equations and the system of Magnetohydrodynamics (MHD) equations with gravitational source term. Since fluid models and kinetic models are related, this leads us to investigate Asymptotic Preserving (AP) schemes for kinetic equations and their ability to preserve stationary solutions. In an attempt to mimic our result for kinetic equations in the context of fluid models, for the isentropic Euler equations we developed an AP scheme in the limit of the Mach number going to zero. The properties of the schemes we developed and its criteria are validated numerically by various test cases from the literature.

Impulsive and Hybrid Dynamical Systems

Impulsive and Hybrid Dynamical Systems
Author: Wassim M. Haddad
Publisher: Princeton University Press
Total Pages: 522
Release: 2014-09-08
Genre: Mathematics
ISBN: 1400865247
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This book develops a general analysis and synthesis framework for impulsive and hybrid dynamical systems. Such a framework is imperative for modern complex engineering systems that involve interacting continuous-time and discrete-time dynamics with multiple modes of operation that place stringent demands on controller design and require implementation of increasing complexity--whether advanced high-performance tactical fighter aircraft and space vehicles, variable-cycle gas turbine engines, or air and ground transportation systems. Impulsive and Hybrid Dynamical Systems goes beyond similar treatments by developing invariant set stability theorems, partial stability, Lagrange stability, boundedness, ultimate boundedness, dissipativity theory, vector dissipativity theory, energy-based hybrid control, optimal control, disturbance rejection control, and robust control for nonlinear impulsive and hybrid dynamical systems. A major contribution to mathematical system theory and control system theory, this book is written from a system-theoretic point of view with the highest standards of exposition and rigor. It is intended for graduate students, researchers, and practitioners of engineering and applied mathematics as well as computer scientists, physicists, and other scientists who seek a fundamental understanding of the rich dynamical behavior of impulsive and hybrid dynamical systems.

Multiscale Methods

Multiscale Methods
Author: Jacob Fish
Publisher: Oxford University Press
Total Pages: 631
Release: 2010
Genre: Mathematics
ISBN: 0199233853
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Small scale features and processes occurring at nanometer and femtosecond scales have a profound impact on what happens at a larger scale and over an extensive period of time. The primary objective of this volume is to reflect the state-of-the-art in multiscale mathematics, modeling, and simulations and to address the following barriers: What is the information that needs to be transferred from one model or scale to another and what physical principles must be satisfied during thetransfer of information? What are the optimal ways to achieve such transfer of information? How can variability of physical parameters at multiple scales be quantified and how can it be accounted for to ensure design robustness?The multiscale approaches in space and time presented in this volume are grouped into two main categories: information-passing and concurrent. In the concurrent approaches various scales are simultaneously resolved, whereas in the information-passing methods the fine scale is modeled and its gross response is infused into the continuum scale. The issue of reliability of multiscale modeling and simulation tools which focus on a hierarchy of multiscale models and an a posteriori model of errorestimation including uncertainty quantification, is discussed in several chapters. Component software that can be effectively combined to address a wide range of multiscale simulations is also described. Applications range from advanced materials to nanoelectromechanical systems (NEMS), biologicalsystems, and nanoporous catalysts where physical phenomena operates across 12 orders of magnitude in time scales and 10 orders of magnitude in spatial scales.This volume is a valuable reference book for scientists, engineers and graduate students practicing in traditional engineering and science disciplines as well as in emerging fields of nanotechnology, biotechnology, microelectronics and energy.

Gale Directory of Publications and Broadcast Media

Gale Directory of Publications and Broadcast Media
Author:
Publisher:
Total Pages: 1470
Release: 1990
Genre: American newspapers
ISBN:
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Identifies specific print and broadcast sources of news and advertising for trade, business, labor, and professionals. Arrangement is geographic with a thumbnail description of each local market. Indexes are classified (by format and subject matter) and alphabetical (by name and keyword).

Interdisciplinary Educational Research In Mathematics and Its Connections to The Arts and Sciences

Interdisciplinary Educational Research In Mathematics and Its Connections to The Arts and Sciences
Author: Bharath Sriraman
Publisher: IAP
Total Pages: 312
Release: 2008-09-01
Genre: Education
ISBN: 1607528878
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The book is based on the recently held Symposium on mathematics and its connections to the arts and sciences, namely the second Mathematics and its Connections to the Arts and Sciences (MACAS2)Symposium in Odense, Denmark (May 29-31, 2007). The chapters are an eclectic collection of interdisciplinary research initiatives undertaken by mathematics educators with implications for practitioners concerned with teaching and learning processes. The papers cover a wide genre of research domains within mathematics education (cognition, modelling, problem solving, teacher education, ethnomathematics, mathematical/statistical literacy, curricular and technological initiatives and research related to science education). The major interdisciplinary themes of the papers in this book are: 1. How can modelling activities be used to foster interdisciplinary projects in the school and university setting? 2. How can the intricate connections between mathematics and physics be used to design and research interdisciplinary activities in schools and the university? 3. How can research within the ethnomathematics domain of mathematics education be linked to critical mathematics education and interdisciplinary projects involving mathematics, art and culture? 4. How can the push for mathematical and statistical literacy be connected to other subjects in the school curricula and emphasized via interdisciplinary activities? 5. What are concrete examples of classroom experiments with empirical data that demonstrate new and unusual connections/relations between mathematics, arts and the sciences with implications for pedagogy? 6. What is the role of technology and new ICT interfaces in linking communities of learners in interdisciplinary activities involving problem solving? The book is an important contribution to the literature on educational initiatives in interdisciplinary education increasing vital for emerging professions of the 21st century.