Series: Systems & Control: Foundations & Applications
2006, Approx. 400 p. 30 illus., Hardcover
ISBN: 0-8176-3255-7
About this book
This self-contained monograph describes basic set-theoretic
methods for control and provides a discussion of their links to
fundamental problems in Lyapunov stability analysis and
stabilization, optimal control, control under constraints,
persistent disturbance rejection, and uncertain systems analysis
and synthesis. New computer technology has catalyzed a resurgence
of research in this area, particularly in the development of set-theoretic
techniques, many of which are computationally demanding.
The work presents several established and potentially new
applications, along with numerical examples and case studies. A
key theme is the trade-off between exact (but computationally
intensive) and approximate (but conservative) solutions to
problems. Mathematical language is kept to the minimum necessary
for the adequate formulation and statement of main concepts.
Efficient numerical algorithms, both in MATLAB and C++, will be
available via the Internet to supplement the presentation and
solution of problems in the book.
"Set-Theoretic Methods in Control" is accessible to
readers familiar with the basics of systems and control theory;
prerequisites such as convexity theory are included. The text
provides a solid foundation of mathematical techniques and
applications and also features avenues for further theoretical
study. While it is aimed primarily at graduate students and
researchers in applied mathematics and engineering, the book will
also appeal to practitioners, since it contains extensive
references to the literature and supplies many recipes for
solving real-world control problems.
Table of contents
Introduction * Lyapunov and Lyapunov-Like Functions * Convex Sets
and Their Representation * Invariant Sets * Dynamic Programming *
Set- Theoretic Estimation * Set-Theoretic Analysis of Dynamic
Systems * Control of Parameter-Varying Systems * Control with
Time-Domain Constraints * (Sub-) Optimal Control * Related Topics
* Bibliography * Index
Series: Progress in Mathematics, Vol. 242
2005, Approx. 300 p., Hardcover
ISBN: 3-7643-7334-2
About this book
The aim of this book is twofold. On the one hand, it gives a
quick, self-contained introduction to Poisson geometry and
related subjects, including singular foliations, Lie groupoids
and Lie algebroids. On the other hand, it presents a
comprehensive treatment of the normal form problem in Poisson
geometry.
Written for:
Graduate students and researchers in differential geometry, Lie
theory and mathematical physics, physicists
Table of contents
Preface.- Generalities on Poisson Structures.- Poisson Cohomology.-
Levi Decomposition.- Linearization of Poisson Structures.-
Multiplicative and Quadratic Poisson Structures.- Nambu
Structures and Singular Foliations.- Lie Groupoids.- Lie
Algebroids.- Appendix.- Bibliography.- Index.
2005, Approx. 270 p. 30 illus., Softcover
ISBN: 0-8176-4396-6
About this textbook
The field of convex geometry has become a fertile subject of
mathematical activity in the past few decades. This exposition,
examining in detail those topics in convex geometry that are
concerned with Euclidean space, is enriched by numerous examples,
illustrations, and exercises, with a good bibliography and index.
The theory of intrinsic volumes for convex bodies, along with the
Hadwiger characterization theorems, whose proofs are based on
beautiful geometric ideas such as the rounding theorems and the
Steiner formula, are treated in Part 1. In Part 2 the reader is
given a survey on curvature and surface area measures and
extensions of the class of convex bodies. Part 3 is devoted to
the important class of star bodies and selectors for convex and
star bodies, including a presentation of two famous problems of
geometric tomography: the Shephard problem and the Busemann?Petty
problem.
Selected Topics in Convex Geometry requires of the reader only a
basic knowledge of geometry, linear algebra, analysis, topology,
and measure theory. The book can be used in the classroom setting
for graduates courses or seminars in convex geometry, geometric
and convex combinatorics, and convex analysis and optimization.
Researchers in pure and applied areas will also benefit from the
book.
Table of contents
Preface to the Polish edition.- Preface to the English edition.-
Introduction.- Part I: Metric spaces.- Subsets of Euclidean space.-
Basic properties of convex sets.- Transformations of the space Kn
of compact convex sets.- Rounding Theorems.- Convex polytopes.-
Functionals on the space Kn. The Steiner Theorem.- The Hadwiger
Theorems.- Applications of the Hadwiger Theorems.- Part II:
Curvature and surface area measures..- Sets with positive reach.
Convexity ring.- Selectors for convex bodies.- Polarity.- Part
III: Star sets. Star bodies.- Intersection bodies.- Selectors for
star bodies.- Exercises to Part I.- Exercises to Part II.-
Exercises to Part III.- References.- Index.
Series: Modeling and Simulation in Science, Engineering and
Technology
2006, Approx. 400 p. 100 illus., Hardcover
ISBN: 0-8176-4376-1
About this textbook
The subject of pattern analysis and recognition pervades many
aspects of our daily lives, including user authentication in
banking, object retrieval from databases in the consumer sector,
and the omnipresent surveillance and security measures around
sensitive areas. Shape analysis, a fundamental building block in
many approaches to these applications, is also used in
statistics, biomedical applications (Magnetic Resonnance Imaging),
and many other related disciplines.
With contributions from some of the leading experts and pioneers
in the field, this self-contained, unified volume is the first
comprehensive treatment of theory, methods, algorithms, and
programs available in a single resource, without the typical
quagmire of vast information scattered over a wide body of
literature. An overview is given of planar and three-dimensional
shape analysis from both a deterministic variational and
statistical perspective with inference applications in pattern
recognition and classification. Developments are discussed from a
rapidly increasing number of research papers in diverse fields,
including the mathematical and physical sciences, engineering,
and medicine.
Part I is an overview of the topic with motivational
applications, quickly initiating a student or new researcher to
the field. Building on existing schools of thoughts, namely
Kendalfs and Grenanderfs, Part II explores the statistical
modeling of landmarks along with a probabilistic modeling of
entire shapes. Part III concentrates on case studies as well as
implementational and practical challenges in real systems.
Extensive illustrations throughout help readers overcome the
sometimes terse technical details of the geometric and
probabilistic formalism. Knowledge of advanced calculus and basic
statistics and probability theory are the only prerequisites for
the reader.
"Statistics and Analysis of Shapes" will be an
essential learning kit for statistical researchers, engineers,
scientists, medical researchers, and students seeking a rapid
introduction to the field. It may be used as a textbook for a
graduate-level special topics course in statistics and signal/image
analysis, or for an intensive short course on shape analysis and
modeling. Experienced researchers and practitioners in academia
and industry will also find this concise source of state-of-the-art
techniques useful
Table of contents
Introduction. Basics of Differential Geometry and Its Relation to
Shape Analysis * Part I. Skeleton and Medial Axis * Analysis of
Shape Deformation * Shape Classification Using Graph Theory *
Principal Geodesic Analysis of Medial Axis Representations * Part
II. Shape Manifolds and Geodesics * Riemannian Metrics on the
Space of Curves * Geodesics on Similarity Invariant Shape
Manifolds * Conformal Metrics on the Space of Curves * Part III.
Modelling * Shape Models and Hausdorff Distances * Probabilistic
Shape Modelling * Shape Learning * Part IV. Shape Analysis and
Other Topics * Integral Invariant Shape Descriptors * Shape
Analysis in FMRI * Geodesics and Shape Analysis in Medical
Imaging * Index
2006, Approx. 220 p. 57 illus., Softcover
ISBN: 0-8176-4398-2
About this textbook
This essentially self-contained, deliberately compact, and user-friendly
textbook is designed for a first, one-semester course in
statistical signal analysis for a broad audience of students in
engineering and the physical sciences. The emphasis throughout is
on fundamental concepts and relationships in the statistical
theory of stationary random signals, explained in a concise, yet
fairly rigorous presentation.
Topics and Features:
* Fourier series and transforms?fundamentally important in random
signal analysis and processing?are developed from scratch,
emphasizing the time-domain vs. frequency-domain duality.
* Basic concepts of probability theory, laws of large numbers,
the stability of fluctuations law, and statistical parametric
inference procedures are presented so that no prior knowledge of
probability and statistics is required; the only prerequisite is
a basic two?three semester calculus sequence.
* Introduction of the fundamental concept of a stationary random
signal and its autocorrelation structure.
* Power spectra of stationary signals and transmission analysis.
* Filter design with optimal signal-to-noise ratio.
* Computer simulation algorithms of stationary random signals
with a given power spectrum density.
* Complementary bibliography for readers who wish to pursue the
study of random signals in greater depth.
* Problems and exercises at the end of each chapter.
Developed by the author over the course of several years of
classroom use, this text may be used by junior/senior
undergraduates or graduate students in electrical, systems,
computer, and biomedical engineering, as well as the physical
sciences. The work is also an excellent resource of educational
and training materials for industrial audiences.
Table of contents
Introduction.- Notation.- Description of Signals.- Spectral
Representation of Deterministic Signals: Fourier Series and
Transforms.- Random Variables and Random Vectors.- Stationary
Signals.- Power Spectra of Random Signals.- Transmission of
Stationary Signals through Linear Systems.- Optimization of
Signal-to-Noise Ratio in Linear Systems.- Gaussian Signals,
Correlation Matrices, and Sample Path Properties.- Computer
Simulation of Stationary Signals.- Bibliography Comments.- Index