Control Theoretic Splines
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| Author | : Magnus Egerstedt |
| Publisher | : Princeton University Press |
| Total Pages | : 232 |
| Release | : 2009-12-07 |
| Genre | : Mathematics |
| ISBN | : 1400833876 |
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.
| Author | : National Aeronautics and Space Administration (NASA) |
| Publisher | : Createspace Independent Publishing Platform |
| Total Pages | : 30 |
| Release | : 2018-07-11 |
| Genre | : |
| ISBN | : 9781722795511 |
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 ...
| Author | : Per Enqvist |
| Publisher | : |
| Total Pages | : 88 |
| Release | : 1994 |
| Genre | : |
| ISBN | : |
| Author | : National Aeronautics and Space Administration (NASA) |
| Publisher | : Createspace Independent Publishing Platform |
| Total Pages | : 46 |
| Release | : 2018-08-20 |
| Genre | : |
| ISBN | : 9781722130060 |
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 ...
| Author | : Gunnar Aronsson |
| Publisher | : |
| Total Pages | : 34 |
| Release | : 1977 |
| Genre | : Control theory |
| ISBN | : |
| Author | : De De Visser |
| Publisher | : Wiley-Blackwell |
| Total Pages | : 600 |
| Release | : 2019-09-06 |
| Genre | : |
| ISBN | : 9781119325611 |
| Author | : L.D. Berkovitz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 315 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 1475760973 |
This book is an introduction to the mathematical theory of optimal control of processes governed by ordinary differential eq- tions. It is intended for students and professionals in mathematics and in areas of application who want a broad, yet relatively deep, concise and coherent introduction to the subject and to its relati- ship with applications. In order to accommodate a range of mathema- cal interests and backgrounds among readers, the material is arranged so that the more advanced mathematical sections can be omitted wi- out loss of continuity. For readers primarily interested in appli- tions a recommended minimum course consists of Chapter I, the sections of Chapters II, III, and IV so recommended in the introductory sec tions of those chapters, and all of Chapter V. The introductory sec tion of each chapter should further guide the individual reader toward material that is of interest to him. A reader who has had a good course in advanced calculus should be able to understand the defini tions and statements of the theorems and should be able to follow a substantial portion of the mathematical development. The entire book can be read by someone familiar with the basic aspects of Lebesque integration and functional analysis. For the reader who wishes to find out more about applications we recommend references [2], [13], [33], [35], and [50], of the Bibliography at the end of the book.
| Author | : Jan C. Willems |
| Publisher | : Springer |
| Total Pages | : 391 |
| Release | : 2010-03-10 |
| Genre | : Science |
| ISBN | : 3540939180 |
This Festschrift, published on the occasion of the sixtieth birthday of Yutaka - mamoto (‘YY’ as he is occasionally casually referred to), contains a collection of articles by friends, colleagues, and former Ph.D. students of YY. They are a tribute to his friendship and his scienti?c vision and oeuvre, which has been a source of inspiration to the authors. Yutaka Yamamoto was born in Kyoto, Japan, on March 29, 1950. He studied applied mathematics and general engineering science at the Department of Applied Mathematics and Physics of Kyoto University, obtaining the B.S. and M.Sc. degrees in 1972 and 1974. His M.Sc. work was done under the supervision of Professor Yoshikazu Sawaragi. In 1974, he went to the Center for Mathematical System T- ory of the University of Florida in Gainesville. He obtained the M.Sc. and Ph.D. degrees, both in Mathematics, in 1976 and 1978, under the direction of Professor Rudolf Kalman.
| Author | : Xiaoming Hu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 376 |
| Release | : 2010-10-29 |
| Genre | : Technology & Engineering |
| ISBN | : 3642112781 |
In this edited collection we commemorate the 60th birthday of Prof. Christopher Byrnes and the retirement of Prof. Anders Lindquist from the Chair of Optimization and Systems Theory at KTH. These papers were presented in part at a 2009 workshop in KTH, Stockholm, honoring the lifetime contributions of Professors Byrnes and Lindquist in various fields of applied mathematics.
| Author | : Alessandro Chiuso |
| Publisher | : Springer |
| Total Pages | : 370 |
| Release | : 2007-10-24 |
| Genre | : Technology & Engineering |
| ISBN | : 3540735704 |
This Festschrift is intended as a homage to our esteemed colleague, friend and maestro Giorgio Picci on the occasion of his sixty-?fth birthday. We have knownGiorgiosince our undergraduatestudies at the University of Padova, wherewe?rst experiencedhisfascinatingteachingin theclass ofSystem Identi?cation. While progressing through the PhD program, then continuing to collaborate with him and eventually becoming colleagues, we have had many opportunitiesto appreciate the value of Giorgio as a professor and a scientist, and chie?y as a person. We learned a lot from him and we feel indebted for his scienti?c guidance, his constant support, encouragement and enthusiasm. For these reasons we are proud to dedicate this book to Giorgio. The articles in the volume will be presented by prominent researchers at the "--Ternational Conference on Modeling, Estimation and Control: A Symposium in Honor of Giorgio Picci on the Occasion of his Sixty-Fifth Birthday", to be held in Venice on October 4-5, 2007. The material covers a broad range of topics in mathematical systems theory, esti- tion, identi?cation and control, re?ecting the wide network of scienti?c relationships established during the last thirty years between the authors and Giorgio. Critical d- cussion of fundamental concepts, close collaboration on speci?c topics, joint research programs in this group of talented people have nourished the development of the?eld, where Giorgio has contributed to establishing several cornerstones.
