E-Book, Englisch, Band 1, 295 Seiten, eBook
Brezinski Computational Aspects of Linear Control
2002
ISBN: 978-1-4613-0261-2
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 1, 295 Seiten, eBook
Reihe: Numerical Methods and Algorithms
ISBN: 978-1-4613-0261-2
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
Introduction.
1. Control of linear systems.
2. Formal orthogonal polynomials.
3. Padé approximations.
4. Transform inversion.
5. Linear algebra issues.
6. Lanczos tridiagonalization process.
7. Systems of linear algebraic equations.
8. Regularization of ill-conditioned systems.
9. Sylvester and riccati equations.
10. Topics on nonlinear differential equations.
11. Appendix: the mathematics of model reduction.
Index.
