A01=Clyde Martin
A01=Magnus Egerstedt
Accuracy and precision
Affine space
Affine variety
Approximation
Author_Clyde Martin
Author_Magnus Egerstedt
Banach space
Bezier curve
Bifurcation theory
Big O notation
Birkhoff interpolation
Boundary value problem
Category=PBW
Chaos theory
Condition number
Constrained optimization
Continuous function
Control theory
Controllability
Convex optimization
Cubic Hermite spline
Data set
Derivative
Dimension (vector space)
Directional derivative
Discrete mathematics
Dynamic programming
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Estimation
Filtering problem (stochastic processes)
Gaussian quadrature
Gradient descent
Gramian matrix
Growth curve (statistics)
Hermite interpolation
Hermite polynomials
Hilbert space
Initial value problem
Integral equation
Iterative method
Karush-Kuhn-Tucker conditions
Least squares
Linear filter
Linear map
Mathematical optimization
Mathematics
Maxima and minima
Monotonic function
Nonlinear programming
Normal distribution
Numerical analysis
Numerical stability
Optimal control
Optimization problem
Orthogonal polynomials
Parameter
Piecewise
Pointwise
Polynomial
Polynomial interpolation
Probability distribution
Quadratic programming
Rate of convergence
Smoothing
Smoothing spline
Special case
Spline (mathematics)
Spline interpolation
Statistic
Stochastic
Telemetry
Theorem
Trapezoidal rule
Without loss of generality
Product details
- ISBN 9780691132969
- Weight: 454g
- Dimensions: 152 x 235mm
- Publication Date: 27 Dec 2009
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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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.
Magnus Egerstedt is associate professor of electrical and computer engineering at Georgia Institute of Technology. Clyde Martin is the P. W. Horn Professor of Mathematics and Statistics at Texas Tech University.
