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Nonlinear Hybrid Continuous/Discrete-Time Models

Author: Marat Akhmet

Publisher: Springer Science & Business Media

Published: 2011-05-03

Total Pages: 225

ISBN-13: 9491216031

The book is mainly about hybrid systems with continuous/discrete-time dynamics. The major part of the book consists of the theory of equations with piece-wise constant argument of generalized type. The systems as well as technique of investigation were introduced by the author very recently. They both generalized known theory about differential equations with piece-wise constant argument, introduced by K. Cook and J. Wiener in the 1980s. Moreover, differential equations with fixed and variable moments of impulses are used to model real world problems. We consider models of neural networks, blood pressure distribution and a generalized model of the cardiac pacemaker. All the results of the manuscript have not been published in any book, yet. They are very recent and united with the presence of the continuous/discrete dynamics of time. It is of big interest for specialists in biology, medicine, engineering sciences, electronics. Theoretical aspects of the book meet very strong expectations of mathematicians who investigate differential equations with discontinuities of any type.

An Introduction to Hybrid Dynamical Systems

Author: Arjan J. van der Schaft

Publisher: Springer

Published: 2007-10-03

Total Pages: 189

ISBN-13: 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.

Hybrid Dynamical Systems

Author: Rafal Goebel

Publisher: Princeton University Press

Published: 2012-03-18

Total Pages: 227

ISBN-13: 1400842638

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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.

Replication of Chaos in Neural Networks, Economics and Physics

Author: Marat Akhmet

Publisher: Springer

Published: 2015-08-13

Total Pages: 468

ISBN-13: 3662475006

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This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics.

4th International Conference on Computational Mathematics and Engineering Sciences (CMES-2019)

Author: Hemen Dutta

Publisher: Springer Nature

Published: 2020-01-10

Total Pages: 332

ISBN-13: 3030391124

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This book gathers original research papers presented at the 4th International Conference on Computational Mathematics and Engineering Sciences, held at Akdeniz University, Antalya, Turkey, on 20–22 April 2019. Focusing on computational methods in science, mathematical tools applied to engineering, mathematical modeling and new aspects of analysis, the book discusses the applications of mathematical modelling in areas such as health science, engineering, computer science, social science, and economics. It also describes a wide variety of analytical, computational, and numerical methods. The conference aimed to foster cooperation between students and researchers in the areas of computational mathematics and engineering sciences, and provide a platform for them to share significant research ideas. This book is a valuable resource for graduate students, researchers and educators interested in the mathematical tools and techniques required for solving various problems arising in science and engineering, and understanding new methods and uses of mathematical analysis.

Constrained Optimal Control of Linear and Hybrid Systems

Author: Francesco Borrelli

Publisher: Springer

Published: 2003-09-04

Total Pages: 206

ISBN-13: 3540362258

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Many practical control problems are dominated by characteristics such as state, input and operational constraints, alternations between different operating regimes, and the interaction of continuous-time and discrete event systems. At present no methodology is available to design controllers in a systematic manner for such systems. This book introduces a new design theory for controllers for such constrained and switching dynamical systems and leads to algorithms that systematically solve control synthesis problems. The first part is a self-contained introduction to multiparametric programming, which is the main technique used to study and compute state feedback optimal control laws. The book's main objective is to derive properties of the state feedback solution, as well as to obtain algorithms to compute it efficiently. The focus is on constrained linear systems and constrained linear hybrid systems. The applicability of the theory is demonstrated through two experimental case studies: a mechanical laboratory process and a traction control system developed jointly with the Ford Motor Company in Michigan.

Smart Applications with Advanced Machine Learning and Human-Centred Problem Design

Author: D. Jude Hemanth

Publisher: Springer Nature

Published: 2023-01-01

Total Pages: 801

ISBN-13: 303109753X

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This book brings together the most recent, quality research papers accepted and presented in the 3rd International Conference on Artificial Intelligence and Applied Mathematics in Engineering (ICAIAME 2021) held in Antalya, Turkey between 1-3 October 2021. Objective of the content is to provide important and innovative research for developments-improvements within different engineering fields, which are highly interested in using artificial intelligence and applied mathematics. As a collection of the outputs from the ICAIAME 2021, the book is specifically considering research outcomes including advanced use of machine learning and careful problem designs on human-centred aspects. In this context, it aims to provide recent applications for real-world improvements making life easier and more sustainable for especially humans. The book targets the researchers, degree students, and practitioners from both academia and the industry.

Regularity and Stochasticity of Nonlinear Dynamical Systems

Author: Dimitri Volchenkov

Publisher: Springer

Published: 2017-06-24

Total Pages: 311

ISBN-13: 3319580620

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This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing on impulsive differential equations, from chaos to order in coupled oscillators, and differential-invariant solutions for automorphic systems, inequality under uncertainty.

Mathematical Modeling and Applications in Nonlinear Dynamics

Author: Albert C.J. Luo

Publisher: Springer

Published: 2016-01-28

Total Pages: 210

ISBN-13: 3319266306

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The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.

Almost Periodicity, Chaos, and Asymptotic Equivalence

Author: Marat Akhmet

Publisher: Springer

Published: 2019-06-20

Total Pages: 360

ISBN-13: 303020572X

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The central subject of this book is Almost Periodic Oscillations, the most common oscillations in applications and the most intricate for mathematical analysis. Prof. Akhmet's lucid and rigorous examination proves these oscillations are a "regular" component of chaotic attractors. The book focuses on almost periodic functions, first of all, as Stable (asymptotically) solutions of differential equations of different types, presumably discontinuous; and, secondly, as non-isolated oscillations in chaotic sets. Finally, the author proves the existence of Almost Periodic Oscillations (asymptotic and bi-asymptotic) by asymptotic equivalence between systems. The book brings readers' attention to contemporary methods for considering oscillations as well as to methods with strong potential for study of chaos in the future. Providing three powerful instruments for mathematical research of oscillations where dynamics are observable and applied, the book is ideal for engineers as well as specialists in electronics, computer sciences, robotics, neural networks, artificial networks, and biology. Distinctively combines results and methods of the theory of differential equations with thorough investigation of chaotic dynamics with almost periodic ingredients; Provides all necessary mathematical basics in their most developed form, negating the need for any additional sources for readers to start work in the area; Presents a unique method of investigation of discontinuous almost periodic solutions in its unified form, employed to differential equations with different types of discontinuity; Develops the equivalence method to its ultimate effective state such that most important theoretical problems and practical applications can be analyzed by the method.