Control theoretic splines [[electronic resource] ] : optimal control, statistics, and path planning / / Magnus Egerstedt and Clyde Martin

• Autore: Egerstedt Magnus
• Pubblicazione: Princeton, : Princeton University Press, c2010
• Edizione: Course Book
• Descrizione fisica: 1 online resource (227 p.)
• Disciplina: 511/.42
• Soggetto topico: Interpolation; Smoothing (Numerical analysis); Smoothing (Statistics); Curve fitting; Splines; Spline theory
• Soggetto non controllato: Accuracy and precision; Affine space; Affine variety; Algorithm; Approximation; Arbitrarily large; B-spline; Banach space; Bernstein polynomial; Bifurcation theory; Big O notation; Birkhoff interpolation; Boundary value problem; Bézier curve; Chaos theory; Computation; Computational problem; Condition number; Constrained optimization; Continuous function (set theory); Continuous function; Control function (econometrics); Control theory; Controllability; Convex optimization; Convolution; Cubic Hermite spline; Data set; Derivative; Differentiable function; Differential equation; Dimension (vector space); Directional derivative; Discrete mathematics; Dynamic programming; Equation; Estimation; Filtering problem (stochastic processes); Gaussian quadrature; Gradient descent; Gramian matrix; Growth curve (statistics); Hermite interpolation; Hermite polynomials; Hilbert projection theorem; Hilbert space; Initial condition; Initial value problem; Integral equation; Iterative method; Karush–Kuhn–Tucker conditions; Kernel method; Lagrange polynomial; Law of large numbers; Least squares; Linear algebra; Linear combination; Linear filter; Linear map; Mathematical optimization; Mathematics; Maxima and minima; Monotonic function; Nonlinear programming; Nonlinear system; Normal distribution; Numerical analysis; Numerical stability; Optimal control; Optimization problem; Ordinary differential equation; Orthogonal polynomials; Parameter; Piecewise; Pointwise; Polynomial interpolation; Polynomial; Probability distribution; Quadratic programming; Random variable; Rate of convergence; Ratio test; Riccati equation; Simpson's rule; Simultaneous equations; Smoothing spline; Smoothing; Smoothness; Special case; Spline (mathematics); Spline interpolation; Statistic; Stochastic calculus; Stochastic; Telemetry; Theorem; Trapezoidal rule; Waypoint; Weight function; Without loss of generality
• Classificazione: SK 880
• Altri autori: MartinClyde
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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
• Sommario/riassunto: 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.
• Titolo autorizzato: Control theoretic splines
• ISBN: 1-282-45796-9; 1-282-93606-9; 9786612936067; 9786612457968; 1-4008-3387-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910807652503321
• Lo trovi qui: Univ. Federico II
• Serie: Princeton series in applied mathematics.