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.
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