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Multi Resolution Methods For Modeling And Control Of Dynamical Systems
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Book Synopsis Multi-Resolution Methods for Modeling and Control of Dynamical Systems by : Puneet Singla
Download or read book Multi-Resolution Methods for Modeling and Control of Dynamical Systems written by Puneet Singla and published by CRC Press. This book was released on 2008-08-01 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unifying the most important methodology in this field, Multi-Resolution Methods for Modeling and Control of Dynamical Systems explores existing approximation methods as well as develops new ones for the approximate solution of large-scale dynamical system problems. It brings together a wide set of material from classical orthogonal function
Book Synopsis Multi-resolution Methods for High Fidelity Modeling and Control Allocation in Large-scale Dynamical Systems by : Puneet Singla
Download or read book Multi-resolution Methods for High Fidelity Modeling and Control Allocation in Large-scale Dynamical Systems written by Puneet Singla and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation introduces novel methods for solving highly challenging modeling and control problems, motivated by advanced aerospace systems. Adaptable, robust and computationally effcient, multi-resolution approximation algorithms based on Radial Basis Function Network and Global-Local Orthogonal Mapping approaches are developed to address various problems associated with the design of large scale dynamical systems. The main feature of the Radial Basis Function Network approach is the unique direction dependent scaling and rotation of the radial basis function via a novel Directed Connectivity Graph approach. The learning of shaping and rotation parameters for the Radial Basis Functions led to a broadly useful approximation approach that leads to global approximations capable of good local approximation for many moderate dimensioned applications. However, even with these refinements, many applications with many high frequency local input/output variations and a high dimensional input space remain a challenge and motivate us to investigate an entirely new approach. The Global-Local Orthogonal Mapping method is based upon a novel averaging process that allows construction of a piecewise continuous global family of local least-squares approximations, while retaining the freedom to vary in a general way the resolution (e.g., degrees of freedom) of the local approximations. These approximation methodologies are compatible with a wide variety of disciplines such as continuous function approximation, dynamic system modeling, nonlinear signal processing and time series prediction. Further, related methods are developed for the modeling of dynamical systems nominally described by nonlinear differential equations and to solve for static and dynamic response of Distributed Parameter Systems in an effcient manner. Finally, a hierarchical control allocation algorithm is presented to solve the control allocation problem for highly over-actuated systems that might arise with the development of embedded systems. The control allocation algorithm makes use of the concept of distribution functions to keep in check the "curse of dimensionality". The studies in the dissertation focus on demonstrating, through analysis, simulation, and design, the applicability and feasibility of these approximation algorithms to a variety of examples. The results from these studies are of direct utility in addressing the "curse of dimensionality" and frequent redundancy of neural network approximation.
Book Synopsis Efficient Modeling and Control of Large-Scale Systems by : Javad Mohammadpour
Download or read book Efficient Modeling and Control of Large-Scale Systems written by Javad Mohammadpour and published by Springer Science & Business Media. This book was released on 2010-06-23 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complexity and dynamic order of controlled engineering systems is constantly increasing. Complex large scale systems (where "large" reflects the system’s order and not necessarily its physical size) appear in many engineering fields, such as micro-electromechanics, manufacturing, aerospace, civil engineering and power engineering. Modeling of these systems often result in very high-order models imposing great challenges to the analysis, design and control problems. "Efficient Modeling and Control of Large-Scale Systems" compiles state-of-the-art contributions on recent analytical and computational methods for addressing model reduction, performance analysis and feedback control design for such systems. Also addressed at length are new theoretical developments, novel computational approaches and illustrative applications to various fields, along with: - An interdisciplinary focus emphasizing methods and approaches that can be commonly applied in various engineering fields -Examinations of applications in various fields including micro-electromechanical systems (MEMS), manufacturing processes, power networks, traffic control "Efficient Modeling and Control of Large-Scale Systems" is an ideal volume for engineers and researchers working in the fields of control and dynamic systems.
Book Synopsis Nonlinear Optimal Control Theory by : Leonard David Berkovitz
Download or read book Nonlinear Optimal Control Theory written by Leonard David Berkovitz and published by CRC Press. This book was released on 2012-08-25 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also discusses Hamilton-Jacobi theory. By providing a sufficient and rigorous treatment of finite dimensional control problems, the book equips readers with the foundation to deal with other types of control problems, such as those governed by stochastic differential equations, partial differential equations, and differential games.
Book Synopsis Introduction to the Calculus of Variations and Control with Modern Applications by : John A. Burns
Download or read book Introduction to the Calculus of Variations and Control with Modern Applications written by John A. Burns and published by CRC Press. This book was released on 2013-08-28 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions and discusses the importance of distinguishing between the necessary and sufficient conditions. In the first part of the text, the author develops the calculus of variations and provides complete proofs of the main results. He explains how the ideas behind the proofs are essential to the development of modern optimization and control theory. Focusing on optimal control problems, the second part shows how optimal control is a natural extension of the classical calculus of variations to more complex problems. By emphasizing the basic ideas and their mathematical development, this book gives you the foundation to use these mathematical tools to then tackle new problems. The text moves from simple to more complex problems, allowing you to see how the fundamental theory can be modified to address more difficult and advanced challenges. This approach helps you understand how to deal with future problems and applications in a realistic work environment.
Book Synopsis Model Reduction of Complex Dynamical Systems by : Peter Benner
Download or read book Model Reduction of Complex Dynamical Systems written by Peter Benner and published by Springer Nature. This book was released on 2021-08-26 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Estimation of Dynamic Systems by : John L. Crassidis
Download or read book Optimal Estimation of Dynamic Systems written by John L. Crassidis and published by CRC Press. This book was released on 2011-10-26 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: An ideal self-study guide for practicing engineers as well as senior undergraduate and beginning graduate students, this book highlights the importance of both physical and numerical modeling in solving dynamics-based estimation problems found in engineering systems, such as spacecraft attitude determination, GPS navigation, orbit determination, and aircraft tracking. With more than 100 pages of new material, this reorganized and expanded edition incorporates new theoretical results, a new chapter on advanced sequential state estimation, and additional examples and exercises. MATLAB codes are available on the book's website.
Book Synopsis Group Inverses of M-Matrices and Their Applications by : Stephen J. Kirkland
Download or read book Group Inverses of M-Matrices and Their Applications written by Stephen J. Kirkland and published by CRC Press. This book was released on 2012-12-18 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas. After introducing sample problems associated with Leslie matrices and stochastic matrices, the authors develop the basic algebraic and spectral properties of the group inverse of a general matrix. They then derive formulas for derivatives of matrix functions and apply the formulas to matrices arising in a demographic setting, including the class of Leslie matrices. With a focus on Markov chains, the text shows how the group inverse of an appropriate M-matrix is used in the perturbation analysis of the stationary distribution vector as well as in the derivation of a bound for the asymptotic convergence rate of the underlying Markov chain. It also illustrates how to use the group inverse to compute and analyze the mean first passage matrix for a Markov chain. The final chapters focus on the Laplacian matrix for an undirected graph and compare approaches for computing the group inverse. Collecting diverse results into a single volume, this self-contained book emphasizes the connections between problems arising in Markov chains, Perron eigenvalue analysis, and spectral graph theory. It shows how group inverses offer valuable insight into each of these areas.
Book Synopsis An Introduction to Partial Differential Equations with MATLAB by : Matthew P. Coleman
Download or read book An Introduction to Partial Differential Equations with MATLAB written by Matthew P. Coleman and published by CRC Press. This book was released on 2016-04-19 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Partial Differential Equations with MATLAB, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat,
Book Synopsis Fourier Series in Several Variables with Applications to Partial Differential Equations by : Victor Shapiro
Download or read book Fourier Series in Several Variables with Applications to Partial Differential Equations written by Victor Shapiro and published by CRC Press. This book was released on 2011-03-28 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Series in Several Variables with Applications to Partial Differential Equations illustrates the value of Fourier series methods in solving difficult nonlinear partial differential equations (PDEs). Using these methods, the author presents results for stationary Navier-Stokes equations, nonlinear reaction-diffusion systems, and quasilinear e
Book Synopsis Advanced Differential Quadrature Methods by : Zhi Zong
Download or read book Advanced Differential Quadrature Methods written by Zhi Zong and published by CRC Press. This book was released on 2009-01-20 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern Tools to Perform Numerical DifferentiationThe original direct differential quadrature (DQ) method has been known to fail for problems with strong nonlinearity and material discontinuity as well as for problems involving singularity, irregularity, and multiple scales. But now researchers in applied mathematics, computational mechanics, and en
Book Synopsis Discovering Evolution Equations with Applications by : Mark McKibben
Download or read book Discovering Evolution Equations with Applications written by Mark McKibben and published by CRC Press. This book was released on 2011-06-03 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversation
Book Synopsis Green's Functions and Linear Differential Equations by : Prem K. Kythe
Download or read book Green's Functions and Linear Differential Equations written by Prem K. Kythe and published by CRC Press. This book was released on 2011-01-21 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Green's Functions and Linear Differential Equations: Theory, Applications, and Computation presents a variety of methods to solve linear ordinary differential equations (ODEs) and partial differential equations (PDEs). The text provides a sufficient theoretical basis to understand Green's function method, which is used to solve initial and boundary
Book Synopsis A Shock-Fitting Primer by : Manuel D. Salas
Download or read book A Shock-Fitting Primer written by Manuel D. Salas and published by CRC Press. This book was released on 2009-12-17 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A defining feature of nonlinear hyperbolic equations is the occurrence of shock waves. While the popular shock-capturing methods are easy to implement, shock-fitting techniques provide the most accurate results. A Shock-Fitting Primer presents the proper numerical treatment of shock waves and other discontinuities. The book begins by recounting the
Book Synopsis Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems by : Jan Awrejcewicz
Download or read book Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems written by Jan Awrejcewicz and published by Springer Science & Business Media. This book was released on 2008-12-26 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the invited papers presented at the 9th International Conference "Dynamical Systems — Theory and Applications" held in Lódz, Poland, December 17-20, 2007, dealing with nonlinear dynamical systems. The conference brought together a large group of outstanding scientists and engineers, who deal with various problems of dynamics encountered both in engineering and in daily life. Topics covered include, among others, bifurcations and chaos in mechanical systems; control in dynamical systems; asymptotic methods in nonlinear dynamics; stability of dynamical systems; lumped and continuous systems vibrations; original numerical methods of vibration analysis; and man-machine interactions. Thus, the reader is given an overview of the most recent developments of dynamical systems and can follow the newest trends in this field of science. This book will be of interest to to pure and applied scientists working in the field of nonlinear dynamics.
Book Synopsis Computing with hp-ADAPTIVE FINITE ELEMENTS by : Leszek Demkowicz
Download or read book Computing with hp-ADAPTIVE FINITE ELEMENTS written by Leszek Demkowicz and published by CRC Press. This book was released on 2007-11-02 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a focus on 1D and 2D problems, the first volume of Computing with hp-ADAPTIVE FINITE ELEMENTS prepared readers for the concepts and logic governing 3D code and implementation. Taking the next step in hp technology, Volume II Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications presents the theoretical foundations of the
Book Synopsis Stochastic Partial Differential Equations by : Pao-Liu Chow
Download or read book Stochastic Partial Differential Equations written by Pao-Liu Chow and published by CRC Press. This book was released on 2007-03-19 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a relatively new area in mathematics, stochastic partial differential equations (PDEs) are still at a tender age and have not yet received much attention in the mathematical community. Filling the void of an introductory text in the field, Stochastic Partial Differential Equations introduces PDEs to students familiar with basic probability theory and Itô's equations, highlighting several computational and analytical techniques. Without assuming specific knowledge of PDEs, the text includes many challenging problems in stochastic analysis and treats stochastic PDEs in a practical way. The author first brings the subject back to its root in classical concrete problems. He then discusses a unified theory of stochastic evolution equations and describes a few applied problems, including the random vibration of a nonlinear elastic beam and invariant measures for stochastic Navier-Stokes equations. The book concludes by pointing out the connection of stochastic PDEs to infinite-dimensional stochastic analysis. By thoroughly covering the concepts and applications of stochastic PDEs at an introductory level, this text provides a guide to current research topics and lays the groundwork for further study.
