Control theoretic splines : optimal control, statistics, and path planning / Magnus Egerstedt and Clyde Martin.

Format:

Book

Author/Creator:

Egerstedt, Magnus.

Contributor:

Martin, Clyde.

Series:

Princeton series in applied mathematics.

Princeton series in applied mathematics

Language:

English

Subjects (All):

Interpolation.

Smoothing (Numerical analysis).

Smoothing (Statistics).

Curve fitting.

Splines.

Spline theory.

Physical Description:

1 online resource (227 p.)

Edition:

Course Book

Place of Publication:

Princeton : Princeton University Press, c2010.

Language Note:

English

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. This book is an excellent resource for students and professionals in control theory, robotics, engineering, computer graphics, econometrics, and any area that requires the construction of curves based on sets of raw data.

Contents:

Frontmatter

Contents

Preface

Chapter One. Introduction

Chapter Two. Control Systems and Minimum Norm Problems

Chapter Three. Eight Fundamental Problems

Chapter Four. Smoothing Splines and Generalizations

Chapter Five. Approximations and Limiting Concepts

Chapter Six. Smoothing Splines with Continuous Data

Chapter Seven. Monotone Smoothing Splines

Chapter Eight. Smoothing Splines as Integral Filters

Chapter Nine. Optimal Transfer between Affine Varieties

Chapter Ten. Path Planning and Telemetry

Chapter Eleven. Node Selection

Bibliography

Index

Notes:

Description based upon print version of record.

Description based on publisher supplied metadata and other sources.

Includes bibliographical references and index.

ISBN:

9786612936067

9786612457968

9781282457966

1282457969

9781282936065

1282936069

9781400833870

1400833876

OCLC:

638859365