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Author: Peter Falb Publisher: Springer Nature ISBN: 0817647236 Category : Science Languages : en Pages : 311
Book Description
Various general techniques have been developed for control and systems problems, many of which involve indirect methods. Because these indirect methods are not always effective, alternative approaches using direct methods are of particular interest and relevance given the advances of computing in recent years. The focus of this book, unique in the literature, is on direct methods, which are concerned with finding actual solutions to problems in control and systems, often algorithmic in nature. Throughout the work, deterministic and stochastic problems are examined from a unified perspective and with considerable rigor. Emphasis is placed on the theoretical basis of the methods and their potential utility in a broad range of control and systems problems. The book is an excellent reference for graduate students, researchers, applied mathematicians, and control engineers and may be used as a textbook for a graduate course or seminar on direct methods in control.
Author: Peter Falb Publisher: Springer Nature ISBN: 0817647236 Category : Science Languages : en Pages : 311
Book Description
Various general techniques have been developed for control and systems problems, many of which involve indirect methods. Because these indirect methods are not always effective, alternative approaches using direct methods are of particular interest and relevance given the advances of computing in recent years. The focus of this book, unique in the literature, is on direct methods, which are concerned with finding actual solutions to problems in control and systems, often algorithmic in nature. Throughout the work, deterministic and stochastic problems are examined from a unified perspective and with considerable rigor. Emphasis is placed on the theoretical basis of the methods and their potential utility in a broad range of control and systems problems. The book is an excellent reference for graduate students, researchers, applied mathematicians, and control engineers and may be used as a textbook for a graduate course or seminar on direct methods in control.
Author: Thomas J. Böhme Publisher: Springer ISBN: 3319513176 Category : Technology & Engineering Languages : en Pages : 549
Book Description
This book assembles new methods showing the automotive engineer for the first time how hybrid vehicle configurations can be modeled as systems with discrete and continuous controls. These hybrid systems describe naturally and compactly the networks of embedded systems which use elements such as integrators, hysteresis, state-machines and logical rules to describe the evolution of continuous and discrete dynamics and arise inevitably when modeling hybrid electric vehicles. They can throw light on systems which may otherwise be too complex or recondite. Hybrid Systems, Optimal Control and Hybrid Vehicles shows the reader how to formulate and solve control problems which satisfy multiple objectives which may be arbitrary and complex with contradictory influences on fuel consumption, emissions and drivability. The text introduces industrial engineers, postgraduates and researchers to the theory of hybrid optimal control problems. A series of novel algorithmic developments provides tools for solving engineering problems of growing complexity in the field of hybrid vehicles. Important topics of real relevance rarely found in text books and research publications—switching costs, sensitivity of discrete decisions and there impact on fuel savings, etc.—are discussed and supported with practical applications. These demonstrate the contribution of optimal hybrid control in predictive energy management, advanced powertrain calibration, and the optimization of vehicle configuration with respect to fuel economy, lowest emissions and smoothest drivability. Numerical issues such as computing resources, simplifications and stability are treated to enable readers to assess such complex systems. To help industrial engineers and managers with project decision-making, solutions for many important problems in hybrid vehicle control are provided in terms of requirements, benefits and risks.
Author: Timothy A. Davis Publisher: SIAM ISBN: 0898716136 Category : Computers Languages : en Pages : 228
Book Description
The sparse backslash book. Everything you wanted to know but never dared to ask about modern direct linear solvers. Chen Greif, Assistant Professor, Department of Computer Science, University of British Columbia.Overall, the book is magnificent. It fills a long-felt need for an accessible textbook on modern sparse direct methods. Its choice of scope is excellent John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara.Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.With a strong emphasis on MATLAB and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.Audience This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing.Preface; Chapter 1: Introduction; Chapter 2: Basic algorithms; Chapter 3: Solving triangular systems; Chapter 4: Cholesky factorization; Chapter 5: Orthogonal methods; Chapter 6: LU factorization; Chapter 7: Fill-reducing orderings; Chapter 8: Solving sparse linear systems; Chapter 9: CSparse; Chapter 10: Sparse matrices in MATLAB; Appendix: Basics of the C programming language; Bibliography; Index.
Author: Bernard Dacorogna Publisher: Springer Science & Business Media ISBN: 3642514405 Category : Mathematics Languages : en Pages : 312
Book Description
In recent years there has been a considerable renewal of interest in the clas sical problems of the calculus of variations, both from the point of view of mathematics and of applications. Some of the most powerful tools for proving existence of minima for such problems are known as direct methods. They are often the only available ones, particularly for vectorial problems. It is the aim of this book to present them. These methods were introduced by Tonelli, following earlier work of Hilbert and Lebesgue. Although there are excellent books on calculus of variations and on direct methods, there are recent important developments which cannot be found in these books; in particular, those dealing with vector valued functions and relaxation of non convex problems. These two last ones are important in appli cations to nonlinear elasticity, optimal design . . . . In these fields the variational methods are particularly effective. Part of the mathematical developments and of the renewal of interest in these methods finds its motivations in nonlinear elasticity. Moreover, one of the recent important contributions to nonlinear analysis has been the study of the behaviour of nonlinear functionals un der various types of convergence, particularly the weak convergence. Two well studied theories have now been developed, namely f-convergence and compen sated compactness. They both include as a particular case the direct methods of the calculus of variations, but they are also, both, inspired and have as main examples these direct methods.
Author: S. I. Kabanikhin Publisher: Walter de Gruyter ISBN: 9789067644167 Category : Mathematics Languages : en Pages : 196
Book Description
The authors consider dynamic types of inverse problems in which the additional information is given by the trace of the direct problem on a (usually time-like) surface of the domain. They discuss theoretical and numerical background of the finite-difference scheme inversion, the linearization method, the method of Gel'fand-Levitan-Krein, the boundary control method, and the projection methodand prove theorems of convergence, conditional stability, and other properties of the mentioned methods.
Author: Ake Bjorck Publisher: SIAM ISBN: 9781611971484 Category : Mathematics Languages : en Pages : 425
Book Description
The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.
Author: Charles D. Fournier Publisher: ISBN: Category : Languages : en Pages : 75
Book Description
The paper describes an approximate numerical method for solution of optimal control problems. It is called a direct method because it deals directly with the functional to be optimized. The approach is based on the Rayleigh-Ritz method for problems in the calculus of variations. It reduces the determination of an optimal control to the solution of a set of simultaneous algebraic equations. Use of a modified Newton algorithm makes it possible to solve these equations rapidly with a relatively small amount of computer memory. The method is illustrated by application to linear and nonlinear problems of optimal operation of chemical reactors. (Author).
Author: Biswa Datta Publisher: Elsevier ISBN: 008053788X Category : Mathematics Languages : en Pages : 736
Book Description
Numerical Methods for Linear Control Systems Design and Analysis is an interdisciplinary textbook aimed at systematic descriptions and implementations of numerically-viable algorithms based on well-established, efficient and stable modern numerical linear techniques for mathematical problems arising in the design and analysis of linear control systems both for the first- and second-order models. Unique coverage of modern mathematical concepts such as parallel computations, second-order systems, and large-scale solutions Background material in linear algebra, numerical linear algebra, and control theory included in text Step-by-step explanations of the algorithms and examples
Author: Peter Falb
Author: Peter Falb
Author: Thomas J. Böhme
Author: John T. Betts
Author: M. Z. Ghanem
Author: Timothy A. Davis
Author: Bernard Dacorogna
Author: S. I. Kabanikhin
Author: Ake Bjorck
Author: Charles D. Fournier
Author: Biswa Datta