Author: Peter Falb
Publisher: Springer Nature
ISBN: 0817647236
Category : Science
Languages : en
Pages : 312
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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
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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
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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
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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
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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: Bulirsch
Publisher: Birkhäuser
ISBN: 3034875398
Category : Science
Languages : en
Pages : 352
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Book Description
"Optimal Control" reports on new theoretical and practical advances essential for analysing and synthesizing optimal controls of dynamical systems governed by partial and ordinary differential equations. New necessary and sufficient conditions for optimality are given. Recent advances in numerical methods are discussed. These have been achieved through new techniques for solving large-sized nonlinear programs with sparse Hessians, and through a combination of direct and indirect methods for solving the multipoint boundary value problem. The book also focuses on the construction of feedback controls for nonlinear systems and highlights advances in the theory of problems with uncertainty. Decomposition methods of nonlinear systems and new techniques for constructing feedback controls for state- and control constrained linear quadratic systems are presented. The book offers solutions to many complex practical optimal control problems.
Author: Biswa Datta
Publisher: Elsevier
ISBN: 008053788X
Category : Mathematics
Languages : en
Pages : 736
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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: I. S. Duff
Publisher: Oxford University Press
ISBN: 0192507516
Category : Mathematics
Languages : en
Pages : 539
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Book Description
The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This second edition is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all examples in the first edition were of order less than 5,000 in the first edition, and are often more than a million in the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done in the last 30 years, some of it by the authors themselves. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms. New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research of the authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.
Author: Curtis R. Vogel
Publisher: SIAM
ISBN: 0898717574
Category : Mathematics
Languages : en
Pages : 195
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Book Description
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Author: Hoai An Le Thi
Publisher: Springer
ISBN: 3030218031
Category : Technology & Engineering
Languages : en
Pages : 1164
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Book Description
This book contains 112 papers selected from about 250 submissions to the 6th World Congress on Global Optimization (WCGO 2019) which takes place on July 8–10, 2019 at University of Lorraine, Metz, France. The book covers both theoretical and algorithmic aspects of Nonconvex Optimization, as well as its applications to modeling and solving decision problems in various domains. It is composed of 10 parts, each of them deals with either the theory and/or methods in a branch of optimization such as Continuous optimization, DC Programming and DCA, Discrete optimization & Network optimization, Multiobjective programming, Optimization under uncertainty, or models and optimization methods in a specific application area including Data science, Economics & Finance, Energy & Water management, Engineering systems, Transportation, Logistics, Resource allocation & Production management. The researchers and practitioners working in Nonconvex Optimization and several application areas can find here many inspiring ideas and useful tools & techniques for their works.
