Download or read book Splines and Control Theory written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-11 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, the relationship between splines and the control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical exponential spline. We have also discovered some new spline functions such as trigonometric splines and the combination of polynomial, exponential and trigonometric splines. The method proposed in this paper is easy to implement. Some numerical experiments are performed to investigate properties of different spline approximations. Zhang, Zhimin and Tomlinson, John and Martin, Clyde Unspecified Center ...
Download or read book Control Theoretic Splines written by Magnus Egerstedt and published by Princeton University Press. This book was released on 2009-12-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Control Theory and Splines Applied to Signature Storage written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-08-20 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this report the problem we are going to study is the interpolation of a set of points in the plane with the use of control theory. We will discover how different systems generate different kinds of splines, cubic and exponential, and investigate the effect that the different systems have on the tracking problems. Actually we will see that the important parameters will be the two eigenvalues of the control matrix. Enqvist, Per Unspecified Center ...
Download or read book Control Theory and Splines written by Per Enqvist and published by . This book was released on 1994 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Perfect Splines and Nonlinear Optimal Control Theory written by Gunnar Aronsson and published by . This book was released on 1977 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book How to Fly an Aircraft with Control Theory and Splines written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-18 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: When trying to fly an aircraft as smoothly as possible it is a good idea to use the derivatives of the pilot command instead of using the actual control. This idea was implemented with splines and control theory, in a system that tries to model an aircraft. Computer calculations in Matlab show that it is impossible to receive enough smooth control signals by this way. This is due to the fact that the splines not only try to approximate the test function, but also its derivatives. A perfect traction is received but we have to pay in very peaky control signals and accelerations. Karlsson, Anders Unspecified Center AIRCRAFT GUIDANCE; CONTROL THEORY; SPLINES; DATA SMOOTHING; FLIGHT CONTROL; STEP FUNCTIONS...
Download or read book Multivariate Splines in Systems and Control Theory written by De De Visser and published by Wiley-Blackwell. This book was released on 2019-09-06 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spline Functions Basic Theory written by Larry Schumaker and published by Cambridge University Press. This book was released on 2007-08-16 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It will be of interest to researchers and students working in applied analysis, numerical analysis, computer science, and engineering. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences. This new edition includes a supplement outlining some of the major advances in the theory since 1981, and some 250 new references. It can be used as the main or supplementary text for courses in splines, approximation theory or numerical analysis.
Download or read book Differential Equations and Control Theory written by Z. Deng and published by CRC Press. This book was released on 2020-11-25 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents the proceedings from the International Conference on Differential Equations and Control Theory, held recently in Wuhan, China. It provides an overview of current developments in a range of topics including dynamical systems, optimal control theory, stochastic control, chaos, fractals, wavelets and ordinary, partial, functional and stochastic differential equations.
Download or read book Spline Models for Observational Data written by Grace Wahba and published by SIAM. This book was released on 1990-09-01 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a number of problems within this framework. Methods for including side conditions and other prior information in solving ill posed inverse problems are provided. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals.
Download or read book Fitting Splines to a Parametric Function written by Alvin Penner and published by Springer. This book was released on 2019-02-23 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Brief investigates the intersections that occur between three different areas of study that normally would not touch each other: ODF, spline theory, and topology. The Least Squares Orthogonal Distance Fitting (ODF) method has become the standard technique used to develop mathematical models of the physical shapes of objects, due to the fact that it produces a fitted result that is invariant with respect to the size and orientation of the object. It is normally used to produce a single optimum fit to a specific object; this work focuses instead on the issue of whether the fit responds continuously as the shape of the object changes. The theory of splines develops user-friendly ways of manipulating six different splines to fit the shape of a simple family of epiTrochoid curves: two types of Bézier curve, two uniform B-splines, and two Beta-splines. This work will focus on issues that arise when mathematically optimizing the fit. There are typically multiple solutions to the ODF method, and the number of solutions can often change as the object changes shape, so two topological questions immediately arise: are there rules that can be applied concerning the relative number of local minima and saddle points, and are there different mechanisms available by which solutions can either merge and disappear, or cross over each other and interchange roles. The author proposes some simple rules which can be used to determine if a given set of solutions is internally consistent in the sense that it has the appropriate number of each type of solution.
Download or read book The Theory of Splines and Their Applications written by J. Harold Ahlberg and published by . This book was released on 1967 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of splines and their applications.
Download or read book Mutual Impact of Computing Power and Control Theory written by M. Kárny and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent rapid developments in computing power, such as parallel processing and neural networks, have stimulated new trends in control. However a discrepancy exists between available computing power and exploitable algorithms obtained classically from control theory. The aim of this book is to address the discrepancy from both the com putational power and control theory viewpoints. Areas such as identification, adaptive control, signal processing and neural networks therefore hold a prominent position in the text presented. The form of the book is such that it should be useful for readers at various levels, particularly those at the research and/or application stage. The book has resulted from the IFAC Workshop on the Mutual Impact of Computing Power and Control Theory, which was held at the Institute of Information Theory and Automation (UTIA), Prague, in September 1992. Organisation of the event was provided jointly by the Department of Adaptive Systems, UTIA, Prague and the School of Engineering and Information Sciences, University of Reading, UK. Selected papers from the Workshop have been chosen to give a good balance across the field, whilst at the same time highlighting important areas for future research. In this way the book represents edited Proceedings from the Workshop. One point, quickly apparent, is the international nature of the presentations themselves, which provide not only a technical appraisal of the field but also inject cultural aspects which are vitally important on the path ahead.
Download or read book Handbook of Splines written by Gheorghe Micula and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a comprehensive introduction to the theory of spline functions, together with some applications to various fields, emphasizing the significance of the relationship between the general theory and its applications. At the same time, the goal of the book is also to provide new ma terial on spline function theory, as well as a fresh look at old results, being written for people interested in research, as well as for those who are interested in applications. The theory of spline functions and their applications is a relatively recent field of applied mathematics. In the last 50 years, spline function theory has undergone a won derful development with many new directions appearing during this time. This book has its origins in the wish to adequately describe this development from the notion of 'spline' introduced by 1. J. Schoenberg (1901-1990) in 1946, to the newest recent theories of 'spline wavelets' or 'spline fractals'. Isolated facts about the functions now called 'splines' can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J.
Download or read book Splines and PDEs From Approximation Theory to Numerical Linear Algebra written by Angela Kunoth and published by Springer. This book was released on 2018-09-20 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods. A wide variety of research topics are covered, ranging from approximation theory to structured numerical linear algebra. More precisely, the book provides (i) a self-contained introduction to B-splines, with special focus on approximation and hierarchical refinement, (ii) a broad survey of numerical schemes for control problems based on B-splines and B-spline-type wavelets, (iii) an exhaustive description of methods for computing and analyzing the spectral distribution of discretization matrices, and (iv) a detailed overview of the mathematical and implementational aspects of isogeometric analysis. The text is the outcome of a C.I.M.E. summer school held in Cetraro (Italy), July 2017, featuring four prominent lecturers with different theoretical and application perspectives. The book may serve both as a reference and an entry point into further research.
Download or read book Fractional Dynamics and Control written by Dumitru Baleanu and published by Springer Science & Business Media. This book was released on 2011-11-19 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science.
Download or read book Approximation and Modeling with B Splines written by Klaus Hollig and published by SIAM. This book was released on 2015-07-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.
