Control theoretic splines optimal control, statistics, and path planning (princeton series in applied mathematics).

Splines, both interpolatory and smoothing, have a long and rich history that has largely been application driven. This book unifies these constructions in a comprehensive and accessible way, drawing from the latest methods and applications to show how they arise naturally in the theory of linear con...

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Bibliographic Details
Main Authors: Egerstedt, Magnus, Martin, Clyde
Format: eBook Book
Language:English
Published: Princeton Princeton University Press 2010
Edition:1
Series:Princeton Series in Applied Mathematics
Subjects:
Curve fitting
Interpolation
Mathematics
Smoothing (Numerical analysis)
Smoothing (Statistics)
Spline theory
Splines
ISBN:0691132968, 9780691132969
Online Access:Get full text
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Summary:Splines, both interpolatory and smoothing, have a long and rich history that has largely been application driven. This book unifies these constructions in a comprehensive and accessible way, drawing from the latest methods and applications to show how they arise naturally in the theory of linear control systems. Magnus Egerstedt and Clyde Martin are leading innovators in the use of control theoretic splines to bring together many diverse applications within a common framework. In this book, they begin with a series of problems ranging from path planning to statistics to approximation. Using the tools of optimization over vector spaces, Egerstedt and Martin demonstrate how all of these problems are part of the same general mathematical framework, and how they are all, to a certain degree, a consequence of the optimization problem of finding the shortest distance from a point to an affine subspace in a Hilbert space. They cover periodic splines, monotone splines, and splines with inequality constraints, and explain how any finite number of linear constraints can be added. This book reveals how the many natural connections between control theory, numerical analysis, and statistics can be used to generate powerful mathematical and analytical tools.
Bibliography:Includes bibliographical references and index
ISBN:0691132968
9780691132969
DOI:10.1515/9781400833870