Leseprobe
* Affiliatelinks/Werbelinks
Links auf reinlesen.de sind sogenannte Affiliate-Links. Wenn du auf so einen Affiliate-Link klickst und über diesen Link einkaufst, bekommt reinlesen.de von dem betreffenden Online-Shop oder Anbieter eine Provision. Für dich verändert sich der Preis nicht.
Control Theoretic Splines
Magnus Egerstedt, Clyde Martin
* Affiliatelinks/Werbelinks
Links auf reinlesen.de sind sogenannte Affiliate-Links. Wenn du auf so einen Affiliate-Link klickst und über diesen Link einkaufst, bekommt reinlesen.de von dem betreffenden Online-Shop oder Anbieter eine Provision. Für dich verändert sich der Preis nicht.
Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Birkhoff interpolation, Integral equation, Smoothing spline, Gramian matrix, Polynomial interpolation, Hilbert space, Affine space, Rate of convergence, Condition number, Gradient descent, Cubic Hermite spline, Initial value problem, Special case, Parameter, Theorem, Hermite interpolation, Data set, Smoothing, Constrained optimization, Polynomial, Approximation, Chaos theory, Linear filter, Boundary value problem, Pointwise, Probability distribution, Linear map, Filtering problem (stochastic processes), Control theory, Mathematics, Nonlinear programming, Karush–Kuhn–Tucker conditions, Numerical stability, Optimization problem, Piecewise, Monotonic function, Dimension (vector space), Spline interpolation, Big O notation, Continuous function, Convex optimization, Bézier curve, Estimation, Growth curve (statistics), Least squares, Controllability, Numerical analysis, Affine variety, Bifurcation theory, Stochastic, Derivative, Banach space, Statistic, Quadratic programming, Normal distribution, Optimal control, Iterative method, Mathematical optimization, Hermite polynomials, Accuracy and precision, Gaussian quadrature, Maxima and minima, Dynamic programming, Spline (mathematics), Trapezoidal rule, Directional derivative, Discrete mathematics, Orthogonal polynomials, Without loss of generality, Telemetry