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Computational aspects of linear control

Many devices (we say dynamical systems or simply systems) behave like black boxes: they receive an input, this input is transformed following some laws (usually a differential equation) and an output is observed. The problem is to regulate the input in order to control the output, that is for obtain...

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Detalles Bibliográficos
Autor principal: Brezinski, Claude
Lenguaje:eng
Publicado: Springer 2002
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-1-4613-0261-2
http://cds.cern.ch/record/2023559
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author Brezinski, Claude
author_facet Brezinski, Claude
author_sort Brezinski, Claude
collection CERN
description Many devices (we say dynamical systems or simply systems) behave like black boxes: they receive an input, this input is transformed following some laws (usually a differential equation) and an output is observed. The problem is to regulate the input in order to control the output, that is for obtaining a desired output. Such a mechanism, where the input is modified according to the output measured, is called feedback. The study and design of such automatic processes is called control theory. As we will see, the term system embraces any device and control theory has a wide variety of applications in the real world. Control theory is an interdisci­ plinary domain at the junction of differential and difference equations, system theory and statistics. Moreover, the solution of a control problem involves many topics of numerical analysis and leads to many interesting computational problems: linear algebra (QR, SVD, projections, Schur complement, structured matrices, localization of eigenvalues, computation of the rank, Jordan normal form, Sylvester and other equations, systems of linear equations, regulariza­ tion, etc), root localization for polynomials, inversion of the Laplace transform, computation of the matrix exponential, approximation theory (orthogonal poly­ nomials, Pad6 approximation, continued fractions and linear fractional transfor­ mations), optimization, least squares, dynamic programming, etc. So, control theory is also a. good excuse for presenting various (sometimes unrelated) issues of numerical analysis and the procedures for their solution. This book is not a book on control.
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spelling cern-20235592021-04-21T20:12:44Zdoi:10.1007/978-1-4613-0261-2http://cds.cern.ch/record/2023559engBrezinski, ClaudeComputational aspects of linear controlMathematical Physics and MathematicsMany devices (we say dynamical systems or simply systems) behave like black boxes: they receive an input, this input is transformed following some laws (usually a differential equation) and an output is observed. The problem is to regulate the input in order to control the output, that is for obtaining a desired output. Such a mechanism, where the input is modified according to the output measured, is called feedback. The study and design of such automatic processes is called control theory. As we will see, the term system embraces any device and control theory has a wide variety of applications in the real world. Control theory is an interdisci­ plinary domain at the junction of differential and difference equations, system theory and statistics. Moreover, the solution of a control problem involves many topics of numerical analysis and leads to many interesting computational problems: linear algebra (QR, SVD, projections, Schur complement, structured matrices, localization of eigenvalues, computation of the rank, Jordan normal form, Sylvester and other equations, systems of linear equations, regulariza­ tion, etc), root localization for polynomials, inversion of the Laplace transform, computation of the matrix exponential, approximation theory (orthogonal poly­ nomials, Pad6 approximation, continued fractions and linear fractional transfor­ mations), optimization, least squares, dynamic programming, etc. So, control theory is also a. good excuse for presenting various (sometimes unrelated) issues of numerical analysis and the procedures for their solution. This book is not a book on control.Springeroai:cds.cern.ch:20235592002
spellingShingle Mathematical Physics and Mathematics
Brezinski, Claude
Computational aspects of linear control
title Computational aspects of linear control
title_full Computational aspects of linear control
title_fullStr Computational aspects of linear control
title_full_unstemmed Computational aspects of linear control
title_short Computational aspects of linear control
title_sort computational aspects of linear control
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-1-4613-0261-2
http://cds.cern.ch/record/2023559
work_keys_str_mv AT brezinskiclaude computationalaspectsoflinearcontrol