Download or read book Tensor Based Dynamical Systems written by Can Chen and published by Springer. This book was released on 2024-04-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive review on tensor algebra, including tensor products, tensor unfolding, tensor eigenvalues, and tensor decompositions. Tensors are multidimensional arrays generalized from vectors and matrices, which can capture higher-order interactions within multiway data. In addition, tensors have wide applications in many domains such as signal processing, machine learning, and data analysis, and the author explores the role of tensors/tensor algebra in tensor-based dynamical systems where system evolutions are captured through various tensor products. The author provides an overview of existing literature on the topic and aims to inspire readers to learn, develop, and apply the framework of tensor-based dynamical systems.

Download or read book Tensor Based Dynamical Systems written by Can Chen and published by Springer Nature. This book was released on with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Manifolds Tensor Analysis and Applications written by Ralph Abraham and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.

Download or read book Tensor Calculus and Analytical Dynamics written by John G. Papastavridis and published by Routledge. This book was released on 2018-12-12 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: tensor calculus in nonholonomic variables Pfaffian nonholonomic constraints related integrability theory of Frobenius The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.

Download or read book Dynamical Systems PDEs and Networks for Biomedical Applications Mathematical Modeling Analysis and Simulations written by André H. Erhardt and published by Frontiers Media SA. This book was released on 2023-02-15 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Tensor Product Model Transformation in Polytopic Model Based Control written by Péter Baranyi and published by CRC Press. This book was released on 2018-09-03 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor Product Model Transformation in Polytopic Model-Based Control offers a new perspective of control system design. Instead of relying solely on the formulation of more effective LMIs, which is the widely adopted approach in existing LMI-related studies, this cutting-edge book calls for a systematic modification and reshaping of the polytopic convex hull to achieve enhanced performance. Varying the convexity of the resulting TP canonical form is a key new feature of the approach. The book concentrates on reducing analytical derivations in the design process, echoing the recent paradigm shift on the acceptance of numerical solution as a valid form of output to control system problems. The salient features of the book include: Presents a new HOSVD-based canonical representation for (qLPV) models that enables trade-offs between approximation accuracy and computation complexity Supports a conceptually new control design methodology by proposing TP model transformation that offers a straightforward way of manipulating different types of convexity to appear in polytopic representation Introduces a numerical transformation that has the advantage of readily accommodating models described by non-conventional modeling and identification approaches, such as neural networks and fuzzy rules Presents a number of practical examples to demonstrate the application of the approach to generate control system design for complex (qLPV) systems and multiple control objectives. The authors’ approach is based on an extended version of singular value decomposition applicable to hyperdimensional tensors. Under the approach, trade-offs between approximation accuracy and computation complexity can be performed through the singular values to be retained in the process. The use of LMIs enables the incorporation of multiple performance objectives into the control design problem and assurance of a solution via convex optimization if feasible. Tensor Product Model Transformation in Polytopic Model-Based Control includes examples and incorporates MATLAB® Toolbox TPtool. It provides a reference guide for graduate students, researchers, engineers, and practitioners who are dealing with nonlinear systems control applications.

Download or read book Data Driven Identification of Networks of Dynamic Systems written by Michel Verhaegen and published by Cambridge University Press. This book was released on 2022-05-12 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to identifying network-connected systems, covering models and methods, and applications in adaptive optics.

Download or read book Tensor Network Contractions written by Shi-Ju Ran and published by Springer Nature. This book was released on 2020-01-27 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.

Download or read book Model Reduction of Nonlinear Mechanical Systems Via Optimal Projection and Tensor Approximation written by Kevin Thomas Carlberg and published by Stanford University. This book was released on 2011 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite the advent and maturation of high-performance computing, high-fidelity physics-based numerical simulations remain computationally intensive in many fields. As a result, such simulations are often impractical for time-critical applications such as fast-turnaround design, control, and uncertainty quantification. The objective of this thesis is to enable rapid, accurate analysis of high-fidelity nonlinear models to enable their use in time-critical settings. Model reduction presents a promising approach for realizing this goal. This class of methods generates low-dimensional models that preserves key features of the high-fidelity model. Such methods have been shown to generate fast, accurate solutions when applied to specialized problems such as linear time-invariant systems. However, model reduction techniques for highly nonlinear systems has been limited primarily to approaches based on the heuristic proper orthogonal decomposition (POD)--Galerkin approach. These methods often generate inaccurate responses because 1) POD--Galerkin does not generally minimize any measure of the system error, and 2) the POD basis is not constructed to minimize errors in the system's outputs of interest. Furthermore, simulation times for these models usually remain large, as reducing the dimension of a nonlinear system does not necessarily reduce its computational complexity. This thesis presents two model reduction techniques that addresses these shortcomings of the POD--Galerkin method. The first method is a `compact POD' approach for computing the small-dimensional trial basis; this approach is applicable to parameterized static systems. The compact POD basis is constructed using a goal-oriented framework that allows sensitivity derivatives to be employed as snapshots. The second method is a Gauss--Newton with approximated tensors (GNAT) method applicable to nonlinear systems. Similar to other POD-based approaches, the GNAT method first executes high-fidelity simulations during a costly `offline' stage; it computes a POD subspace that optimally represents the state as observed during these simulations. To compute fast, accurate `online' solutions, the method introduces two approximations that satisfy optimality and consistency conditions. First, the method decreases the system dimension by searching for the solutions in the low-dimensional POD subspace. As opposed to performing a Galerkin projection, the method handles the resulting overdetermined system of equations arising at each time step by formulating a least-squares problem; this ensures that a measure of the system error (i.e. the residual) is minimized. Second, the method decreases the model's computational complexity by approximating the residual and Jacobian using the `gappy POD' technique; this requires computing only a few rows of the approximated quantities. For computational mechanics problems, the GNAT method leads to the concept of a sample mesh: the subset of the mesh needed to compute the selected rows of the residual and Jacobian. Because the reduced-order model uses only the sample mesh for computations, the online stage requires minimal computational resources.

Download or read book From Dimension Free Matrix Theory to Cross Dimensional Dynamic Systems written by Daizhan Cheng and published by Academic Press. This book was released on 2019-05-18 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems illuminates the underlying mathematics of semi-tensor product (STP), a generalized matrix product that extends the conventional matrix product to two matrices of arbitrary dimensions. Dimension-varying systems feature prominently across many disciplines, and through innovative applications its newly developed theory can revolutionize large data systems such as genomics and biosystems, deep learning, IT, and information-based engineering applications. Provides, for the first time, cross-dimensional system theory that is useful for modeling dimension-varying systems. Offers potential applications to the analysis and control of new dimension-varying systems. Investigates the underlying mathematics of semi-tensor product, including the equivalence and lattice structure of matrices and monoid of matrices with arbitrary dimensions.

Download or read book High Performance Tensor Computations in Scientific Computing and Data Science written by Edoardo Angelo Di Napoli and published by Frontiers Media SA. This book was released on 2022-11-08 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dynamic Network Representation Based on Latent Factorization of Tensors written by Hao Wu and published by Springer Nature. This book was released on 2023-03-07 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: A dynamic network is frequently encountered in various real industrial applications, such as the Internet of Things. It is composed of numerous nodes and large-scale dynamic real-time interactions among them, where each node indicates a specified entity, each directed link indicates a real-time interaction, and the strength of an interaction can be quantified as the weight of a link. As the involved nodes increase drastically, it becomes impossible to observe their full interactions at each time slot, making a resultant dynamic network High Dimensional and Incomplete (HDI). An HDI dynamic network with directed and weighted links, despite its HDI nature, contains rich knowledge regarding involved nodes’ various behavior patterns. Therefore, it is essential to study how to build efficient and effective representation learning models for acquiring useful knowledge. In this book, we first model a dynamic network into an HDI tensor and present the basic latent factorization of tensors (LFT) model. Then, we propose four representative LFT-based network representation methods. The first method integrates the short-time bias, long-time bias and preprocessing bias to precisely represent the volatility of network data. The second method utilizes a proportion-al-integral-derivative controller to construct an adjusted instance error to achieve a higher convergence rate. The third method considers the non-negativity of fluctuating network data by constraining latent features to be non-negative and incorporating the extended linear bias. The fourth method adopts an alternating direction method of multipliers framework to build a learning model for implementing representation to dynamic networks with high preciseness and efficiency.

Download or read book Journal of Dynamic Systems Measurement and Control written by and published by . This book was released on 1999 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publishes theoretical and applied original papers in dynamic systems. Theoretical papers present new theoretical developments and knowledge for controls of dynamical systems together with clear engineering motivation for the new theory. Applied papers include modeling, simulation, and corroboration of theory with emphasis on demonstrated practicality.

Download or read book Tensor Eigenvalues and Their Applications written by Liqun Qi and published by Springer. This book was released on 2018-03-30 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.

Download or read book Mechatronics by Bond Graphs written by Vjekoslav Damić and published by Springer Science & Business Media. This book was released on 2003 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: CD-ROM contains: the program "BondSim Pack."

Download or read book Dynamic Analysis of Robot Manipulators written by Constantinos A. Balafoutis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this monograph is to present computationally efficient algorithms for solving basic problems in robot manipulator dynamics. In par ticular, the following problems of rigid-link open-chain manipulator dynam ics are considered : i) computation of inverse dynamics, ii) computation of forward dynamics, and iii) generation of linearized dynamic models. Com putationally efficient solutions of these problems are prerequisites for real time robot applications and simulations. Cartesian tensor analysis is the mathematical foundation on which the above mentioned computational algorithms are based. In particular, it is shown in this monograph that by exploiting the relationships between second order Cartesian tensors and their vector invariants, a number of new tensor vector identities can be obtained. These identities enrich the theory of Carte sian tensors and allow us to manipulate complex Cartesian tensor equations effuctively. Moreover, based on these identities the classical vector descrip tion for the Newton-Euler equations of rigid body motion are rewritten in an equivalent tensor formulation which is shown to have computational advan tages over the classical vector formulation. Thus, based on Cartesian tensor analysis, a conceptually simple, easy to implement and computationally efficient tensor methodology is presented in this monograph for studying classical rigid body dynamics. XlI Application of this tensor methodology to the dynamic analysis of rigid-link open-chain robot manipulators is simple and leads to an efficient fonnulation of the dynamic equations of motion.

Download or read book Advances in Dynamical Systems Theory Models Algorithms and Applications written by Bruno Carpentieri and published by BoD – Books on Demand. This book was released on 2021-07-28 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of modern dynamical systems dates back to 1890 with studies by Poincaré on celestial mechanics. The tradition was continued by Birkhoff in the United States with his pivotal work on periodic orbits, and by the Moscow School in Russia (Liapunov, Andronov, Pontryagin). In the 1960s the field was revived by the emergence of the theory of chaotic attractors, and in modern years by accurate computer simulations. This book provides an overview of recent developments in the theory of dynamical systems, presenting some significant advances in the definition of new models, computer algorithms, and applications. Researchers, engineers and graduate students in both pure and applied mathematics will benefit from the chapters collected in this volume.