Series: Communications and Control Engineering
Originally published as volume 242 in the series: Lecture Notes in Control and Information Sciences
2007, XVI, 178 p., 16 illus., Hardcover
ISBN: 978-1-84628-594-3
About this book
A self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students.
The most popular treatment of control for nonlinear systems is from the viewpoint of differential geometry yet this approach proves not to be the most natural when considering problems like dynamic feedback and realization. Professors Conte, Moog and Perdon develop an alternative linear-algebraic strategy based on the use of vector spaces over suitable fields of nonlinear functions. This algebraic perspective is complementary to, and parallel in concept with, its more celebrated differential-geometric counterpart.
Algebraic Methods for Nonlinear Control Systems describes a wide range of results, some of which can be derived using differential geometry but many of which cannot. They include:
* classical and generalized realization in the nonlinear context;
* accessibility and observability recast within the linear-algebraic setting;
* discussion and solution of basic feedback problems like input-to-output
linearization, input-to-state linearization, non-interacting control and
disturbance decoupling;
* results for dynamic and static state and output feedback.
Dynamic feedback and realization are shown to be dealt with and solved much more easily within the algebraic framework.
Originally published as Nonlinear Control Systems, 1-85233-151-8, this second edition has been completely revised with new text ? chapters on modeling and systems structure are expanded and that on output feedback added de novo ? examples and exercises. The book is divided into two parts: the first being devoted to the necessary methodology and the second to an exposition of applications to control problems.
Table of contents
Series: Lecture Notes in Mathematics Vol. 1908
Subseries: Ecole d'Ete Probabilit.Saint-Flour
2007, XVIII, 116 p., 3 illus., Softcover
ISBN: 978-3-540-71284-8
About this book
Each year young mathematicians congregate in Saint Flour, France, and listen to extended lecture courses on new topics in Probability Theory.
The goal of these notes, representing a course given by Terry Lyons in 2004, is to provide a straightforward and self supporting but minimalist account of the key results forming the foundation of the theory of rough paths. The proofs are similar to those in the existing literature, but have been refined with the benefit of hindsight. The theory of rough paths aims to create the appropriate mathematical framework for expressing the relationships between evolving systems, by extending classical calculus to the natural models for noisy evolving systems, which are often far from differentiable
Table of contents
Series: Lecture Notes in Mathematics , Vol. 1912
Originally published by Editura Efemeride, Baia Mare, Romania, 2002
2007, XVI, 326 p., Softcover
ISBN: 978-3-540-72233-5
About this book
The aim of this monograph is to give a unified introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. It summarizes the most significant contributions in the area by presenting, for each iterative method considered (Picard iteration, Krasnoselskij iteration, Mann iteration, Ishikawa iteration etc.), some of the most relevant, interesting, representative and actual convergence theorems. Applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods, are also presented. Due to the explosive number of research papers on the topic (in the last 15 years only, more than one thousand articles related to the subject were published), it was felt that such a monograph was imperatively necessary. The volume is useful for authors, editors, and reviewers. It introduces concrete criteria for evaluating and judging the plethora of published papers.
Table of contents
Series: Theoretical and Mathematical Physics
Originally published as volume 322 in the series: Lecture Notes in Physics
2007, Approx. 230 p., Hardcover
ISBN: 978-3-540-71174-2
About this book
This book gives an introduction to modern geometry. Starting from an elementary level the author develops deep geometrical concepts, playing an important role nowadays in contemporary theoretical physics. He presents various techniques and viewpoints, thereby showing the relations between the alternative approaches.
At the end of each chapter suggestions for further reading are given to allow the reader to study the touched topics in greater detail.
This second edition of the book contains two additional more advanced geometric techniques: (1) The modern language and modern view of Algebraic Geometry and (2) Mirror Symmetry.
The book grew out of lecture courses. The presentation style is therefore similar to a lecture. Graduate students of theoretical and mathematical physics will appreciate this book as textbook. Students of mathematics who are looking for a short introduction to the various aspects of modern geometry and their interplay will also find it useful. Researchers will esteem the book as reliable reference.
Table of contents
Introduction.- Manifolds.- Topology of Riemann Surfaces.- Analytic Structure.- Differentials and Integration.- Tori and Jacobians.- Projective Varieties.- Moduli Spaces of Curves.- Vector Bundles, Sheaves and Cohomology.- The Theorem of Riemann-Roch for Line Bundles.- The Mumford Isomorphism on the Moduli Space.- Modern Algebraic Geometry.- Schemes.- Hodge Decomposition and Kahler Manifold.- Calabi-Yau Manifolds and Mirror Symmetry.
Collection: Mathematiques et Applications , Vol. 59
2007, Approx. 320 p., Broche
ISBN: 978-3-540-71646-4
A propos de ce livre
Les equations polynomiales apparaissent dans de nombreux domaines, pour modeliser des contraintes geometriques, des relations entre des grandeurs physiques, ou encore des proprietes satisfaites par certaines inconnues. Cet ouvrage est une introduction aux methodes algebriques permettant de resoudre ce type d'equations. Nous montrons comment la geometrie des varietes algebriques definies par ces equations, leur dimension, leur degre, ou leurs composantes peuvent se deduire des proprietes des algebres quotients correspondantes. Nous abordons pour cela des methodes de la geometrie algebrique effective, telles que les bases de Grobner, la resolution par valeurs et vecteurs propres, les resultants, les bezoutiens, la dualite, les algebres de Gorenstein et les residus algebriques. Ces methodes sont accompagnees d'algorithmes, d'exemples et d'exercices, illustrant leurs applications.
Sommaire
Introduction.- 1. Equations, Ideaux, Varietes.- 2. Calcul dans une algebre quotient.- 3. Dimension et degre d'une variete algebrique.- 4. Algebres de dimension 0.- 5. Theorie des resultants.- 6. Application des resultants.- 7. Dualite.- 8. Algebres de Gorenstein.- 9. Residu algebrique.- 10. Calcul du residu et applications.- Liste des algorithmes.- Liste des notations.- Bibliographie.- Index.
Series: Lecture Notes in Mathematics , Vol. 1909
2007, XLIII, 252 p., Softcover
ISBN: 978-3-540-71806-2
About this book
This monograph is Part 1 of a book project intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization, with application to knot theory.
Although Jorgensen's original work was not published in complete form, it has been a source of inspiration. In particular, it has motivated and guided Thurston's revolutionary study of low-dimensional geometric topology.
In this monograph, we give an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.
Table of contents
Jorgensen's picture of quasifuchsian punctured torus groups.- Fricke surfaces and PSL(2,C)-representations.- Labeled representations and associated complexes.- Chain rule and side parameter.- Special examples.- Reformulation of the main theorem and outline of the proof.- Openness.- Closedness.- Algebraic roots and geometric roots.- Appendix.- References.- Index.