Nonlinear Model Reduction By Moment Matching

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Nonlinear Model Reduction By Moment Matching

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Author : Giordano Scarciotti
language : en
Publisher:
Release Date : 2017

Nonlinear Model Reduction By Moment Matching written by Giordano Scarciotti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Electronic books categories.

Mathematical models are at the core of modern science and technology. An accurate description of behaviors, systems and processes often requires the use of complex models which are difficult to analyze and control. To facilitate analysis of and design for complex systems, model reduction theory and tools allow determining "simpler" models which preserve some of the features of the underlying complex description. A large variety of techniques, which can be distinguished depending on the features which are preserved in the reduction process, has been proposed to achieve this goal. One such a method is the moment matching approach. This monograph focuses on the problem of model reduction by moment matching for nonlinear systems. The central idea of the method is the preservation, for a prescribed class of inputs and under some technical assumptions, of the steady-state output response of the system to be reduced. We present the moment matching approach from this vantage point, covering the problems of model reduction for nonlinear systems, nonlinear time-delay systems, data-driven model reduction for nonlinear systems and model reduction for "discontinuous" input signals. Throughout the monograph linear systems, with their simple structure and strong properties, are used as a paradigm to facilitate understanding of the theory and provide foundation of the terminology and notation. The text is enriched by several numerical examples, physically motivated examples and with connections to well-established notions and tools, such as the phasor transform.

Nonlinear Model Reduction By Moment Matching

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Author : Giordano Scarciotti
language : en
Publisher:
Release Date : 2017-07-28

Nonlinear Model Reduction By Moment Matching written by Giordano Scarciotti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-28 with Technology & Engineering categories.

Reduced order models, or model reduction, have been used in many technologically advanced areas to ensure the associated complicated mathematical models remain computable. For instance, reduced order models are used to simulate weather forecast models and in the design of very large scale integrated circuits and networked dynamical systems. For linear systems, the model reduction problem has been addressed from several perspectives and a comprehensive theory exists. Although many results and efforts have been made, at present there is no complete theory of model reduction for nonlinear systems or, at least, not as complete as the theory developed for linear systems. This monograph presents, in a uniform and complete fashion, moment matching techniques for nonlinear systems. This includes extensive sections on nonlinear time-delay systems; moment matching from input/output data and the limitations of the characterization of moment based on a signal generator described by differential equations. Each section is enriched with examples and is concluded with extensive bibliographical notes. This monograph provides a comprehensive and accessible introduction into model reduction for researchers and students working on non-linear systems.

Linear And Nonlinear Model Order Reduction For Numerical Simulation Of Electric Circuits

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Author : Kasra Mohaghegh
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2010

Linear And Nonlinear Model Order Reduction For Numerical Simulation Of Electric Circuits written by Kasra Mohaghegh and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

Increasing complexity combined with decreasing geometrical sizes in electric circuit design lead to high dimensional dynamical models to be considered by EDA tools. Model order reduction (MOR) has become a popular strategy to decrease the problem's size while preserving its crucial properties. MOR shall achieve accurate statements on a circuit's behavior within an affordable amount of computational time. Just recently, MOR techniques are designed to consider the differential algebraic nature of the underlying models. We present an approach based on an e-embedding, i.e., a strategy applied in the construction of numerical integration schemes for differential algebraic equations (DAEs). The system of DAEs is transformed into an artificial system of ordinary differential equations (ODEs), since MOR schemes for ODEs can be applied now. We construct, analyze and test different strategies with respect to the usage of the parameter e that transforms the DAEs into ODEs. Moreover, accurate mathematical models for MOS-devices introduce highly nonlinear equations. As the packing density of devices is growing in circuit design, huge nonlinear systems appear in practice. It follows an increasing demand for reduced order modeling of nonlinear problems. In the thesis, we also review the status of existing techniques for nonlinear MOR by investigating the performance of the schemes applied in circuit simulation.

Analysis And Design Of Nonlinear Control Systems

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Author : Alessandro Astolfi
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-13

Analysis And Design Of Nonlinear Control Systems written by Alessandro Astolfi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-13 with Technology & Engineering categories.

This book is a tribute to Prof. Alberto Isidori on the occasion of his 65th birthday. Prof. Isidori’s proli?c, pioneering and high-impact research activity has spanned over 35 years. Throughout his career, Prof. Isidori has developed ground-breaking results, has initiated researchdirections and has contributed towardsthe foundationofnonlinear controltheory.In addition,his dedication to explain intricate issues and di?cult concepts in a simple and rigorous way and to motivate young researchers has been instrumental to the intellectual growth of the nonlinear control community worldwide. The volume collects 27 contributions written by a total of 52 researchers. The principal author of each contribution has been selected among the - searchers who have worked with Prof. Isidori, have in?uenced his research activity, or have had the privilege and honour of being his PhD students. The contributions address a signi?cant number of control topics, including th- retical issues, advanced applications, emerging control directions and tutorial works. The diversity of the areas covered, the number of contributors and their international standing provide evidence of the impact of Prof. Isidori in the control and systems theory communities. The book has been divided into six parts: System Analysis, Optimization Methods, Feedback Design, Regulation, Geometric Methods and Asymptotic Analysis, re?ecting important control areas which have been strongly in- enced and, in some cases, pioneered by Prof. Isidori.

Feedback Stabilization Of Controlled Dynamical Systems

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Author : Nicolas Petit
language : en
Publisher: Springer
Release Date : 2017-03-23

Feedback Stabilization Of Controlled Dynamical Systems written by Nicolas Petit and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-23 with Technology & Engineering categories.

This book is a tribute to Professor Laurent Praly and follows on from a workshop celebrating the occasion of his 60th birthday. It presents new and unified visions of the numerous problems that Laurent Praly has worked on in his prolific career: adaptive control, output feedback and observers, stability and stabilization. His main contributions are the central topic of this book. The book collects contributions written by prominent international experts in the control community, addressing a rich variety of topics: emerging ideas, advanced applications, and theoretical concepts. Organized in three sections, the first section covers the field of adaptive control, where Laurent Praly started his career. The second section focuses on stabilization and output feedback, which is also the topic of the second half of his career. Lastly, the third section presents the emerging research that will form Laurent Praly’s scientific legacy.

Model Reduction Of Complex Dynamical Systems

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Author : Peter Benner
language : en
Publisher: Springer Nature
Release Date : 2021-08-26

Model Reduction Of Complex Dynamical Systems written by Peter Benner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-26 with Mathematics categories.

This contributed volume presents some of the latest research related to model order reduction of complex dynamical systems with a focus on time-dependent problems. Chapters are written by leading researchers and users of model order reduction techniques and are based on presentations given at the 2019 edition of the workshop series Model Reduction of Complex Dynamical Systems – MODRED, held at the University of Graz in Austria. The topics considered can be divided into five categories: system-theoretic methods, such as balanced truncation, Hankel norm approximation, and reduced-basis methods; data-driven methods, including Loewner matrix and pencil-based approaches, dynamic mode decomposition, and kernel-based methods; surrogate modeling for design and optimization, with special emphasis on control and data assimilation; model reduction methods in applications, such as control and network systems, computational electromagnetics, structural mechanics, and fluid dynamics; and model order reduction software packages and benchmarks. This volume will be an ideal resource for graduate students and researchers in all areas of model reduction, as well as those working in applied mathematics and theoretical informatics.

Reduced Order Modeling Rom For Simulation And Optimization

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Author : Winfried Keiper
language : en
Publisher: Springer
Release Date : 2018-04-11

Reduced Order Modeling Rom For Simulation And Optimization written by Winfried Keiper and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-11 with Mathematics categories.

This edited monograph collects research contributions and addresses the advancement of efficient numerical procedures in the area of model order reduction (MOR) for simulation, optimization and control. The topical scope includes, but is not limited to, new out-of-the-box algorithmic solutions for scientific computing, e.g. reduced basis methods for industrial problems and MOR approaches for electrochemical processes. The target audience comprises research experts and practitioners in the field of simulation, optimization and control, but the book may also be beneficial for graduate students alike.

Two Sided Moment Matching Methods For Nonlinear Model Reduction

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Author : Peter Benner
language : en
Publisher:
Release Date : 2012

Two Sided Moment Matching Methods For Nonlinear Model Reduction written by Peter Benner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.

Abstract: In this paper, we discuss a recently introduced approach for nonlinear model order reduction. The new method is motivated by the concept of moment matching known from model reduction techniques for linear systems and can be generalized by means of generalized transfer functions arising for a large class of smooth nonlinear control affine dynamical systems. We will extend the existing concepts by making use of some basic tools known from tensor theory. This will allow a more efficient computation of the reduced-order model as well as the possibility of constructing two-sided projection methods which are theoretically shown to yield more accurate reduced-order models. Moreover, we will test both, one-sided and two-sided projection methods, on several semi-discretized nonlinear partial differential equations which already have been used as test examples in the context of nonlinear model reduction and compare them with the common nonlinear reduction technique proper orthogonal decomposition. We will further point out the main advantages and drawbacks of our new method.

Realization And Model Reduction Of Dynamical Systems

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Author : Christopher Beattie
language : en
Publisher: Springer Nature
Release Date : 2022-06-09

Realization And Model Reduction Of Dynamical Systems written by Christopher Beattie and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Science categories.

This book celebrates Professor Thanos Antoulas's 70th birthday, marking his fundamental contributions to systems and control theory, especially model reduction and, more recently, data-driven modeling and system identification. Model reduction is a prominent research topic with wide ranging scientific and engineering applications.

Advances In Analog Circuits

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Author : Esteban Tlelo-Cuautle
language : en
Publisher: BoD – Books on Demand
Release Date : 2011-02-02

Advances In Analog Circuits written by Esteban Tlelo-Cuautle and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-02 with Technology & Engineering categories.

This book highlights key design issues and challenges to guarantee the development of successful applications of analog circuits. Researchers around the world share acquired experience and insights to develop advances in analog circuit design, modeling and simulation. The key contributions of the sixteen chapters focus on recent advances in analog circuits to accomplish academic or industrial target specifications.