Numerical Methods for Large-Scale Linear Time-Varying Control Systems and related Differential Matrix Equations PDF Download
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Author: Norman Lang
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832547002
Category : Mathematics
Languages : en
Pages : 232
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Book Description
This thesis is concerned with the linear-quadratic optimal control and model order reduction (MOR) of large-scale linear time-varying (LTV) control systems. In the first two parts, particular attention is paid to a tracking-type finite-time optimal control problem with application to an inverse heat conduction problem and the balanced truncation (BT) MOR method for LTV systems. In both fields of application the efficient solution of differential matrix equations (DMEs) is of major importance. The third and largest part deals with the application of implicit time integration methods to these matrix-valued ordinary differential equations. In this context, in particular, the rather new class of peer methods is introduced. Further, for the efficient solution of large-scale DMEs, in practice low-rank solution strategies are inevitable. Here, low-rank time integrators, based on a symmetric indefinte factored representation of the right hand sides and the solution approximations of the DMEs, are presented. In contrast to the classical low-rank Cholesky-type factorization, this avoids complex arithmetic and tricky implementations and algorithms. Both low-rank approaches are compared for numerous implicit time integration methods.
Author: Norman Lang
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832547002
Category : Mathematics
Languages : en
Pages : 232
Get Book Here
Book Description
This thesis is concerned with the linear-quadratic optimal control and model order reduction (MOR) of large-scale linear time-varying (LTV) control systems. In the first two parts, particular attention is paid to a tracking-type finite-time optimal control problem with application to an inverse heat conduction problem and the balanced truncation (BT) MOR method for LTV systems. In both fields of application the efficient solution of differential matrix equations (DMEs) is of major importance. The third and largest part deals with the application of implicit time integration methods to these matrix-valued ordinary differential equations. In this context, in particular, the rather new class of peer methods is introduced. Further, for the efficient solution of large-scale DMEs, in practice low-rank solution strategies are inevitable. Here, low-rank time integrators, based on a symmetric indefinte factored representation of the right hand sides and the solution approximations of the DMEs, are presented. In contrast to the classical low-rank Cholesky-type factorization, this avoids complex arithmetic and tricky implementations and algorithms. Both low-rank approaches are compared for numerous implicit time integration methods.
Author: Yousef Saad
Publisher: SIAM
ISBN: 0898715342
Category : Mathematics
Languages : en
Pages : 537
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Book Description
Mathematics of Computing -- General.
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: Randall J. LeVeque
Publisher: SIAM
ISBN: 9780898717839
Category : Mathematics
Languages : en
Pages : 356
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Book Description
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
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Category : Science
Languages : en
Pages : 250
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Book Description
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Category : Aeronautics
Languages : en
Pages : 244
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Book Description
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Category : Mechanics, Applied
Languages : en
Pages : 628
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Book Description
Author: William S. Levine
Publisher: CRC Press
ISBN: 142007363X
Category : Technology & Engineering
Languages : en
Pages : 788
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Book Description
At publication, The Control Handbook immediately became the definitive resource that engineers working with modern control systems required. Among its many accolades, that first edition was cited by the AAP as the Best Engineering Handbook of 1996. Now, 15 years later, William Levine has once again compiled the most comprehensive and authoritative resource on control engineering. He has fully reorganized the text to reflect the technical advances achieved since the last edition and has expanded its contents to include the multidisciplinary perspective that is making control engineering a critical component in so many fields. Now expanded from one to three volumes, The Control Handbook, Second Edition brilliantly organizes cutting-edge contributions from more than 200 leading experts representing every corner of the globe. The first volume, Control System Fundamentals, offers an overview for those new to the field but is also of great value to those across any number of fields whose work is reliant on but not exclusively dedicated to control systems. Covering mathematical fundamentals, defining principles, and basic system approaches, this volume: Details essential background, including transforms and complex variables Includes mathematical and graphical models used for dynamical systems Covers analysis and design methods and stability testing for continuous-time systems Delves into digital control and discrete-time systems, including real-time software for implementing feedback control and programmable controllers Analyzes design methods for nonlinear systems As with the first edition, the new edition not only stands as a record of accomplishment in control engineering but provides researchers with the means to make further advances. Progressively organized, the other two volumes in the set include: Control System Applications Control System Advanced Methods
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Category : Computers
Languages : en
Pages : 488
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Book Description
Author: Uri M. Ascher
Publisher: SIAM
ISBN: 0898716527
Category : Mathematics
Languages : en
Pages : 403
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Book Description
Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.
