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Tautological Control SystemsIntroduction, Motivation, and Background

Tautological Control Systems: Introduction, Motivation, and Background [One can study nonlinear control theory from the point of view of applications, or from a more fundamental point of view, where system structure is a key element. From the practical point of view, questions that arise are often of the form, “How can we...”, for example, “How can we steer a system from point A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A$$\end{document} to point B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B$$\end{document}?” or, “How can we stabilise this unstable equilibrium point?” or, “How can we manoeuvre this vehicle in the most efficient manner?” From a fundamental point of view, the problems are often of a more existential nature, with, “How can we” replaced with, “Can we”. These existential questions are often very difficult to answer in any sort of generality.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Tautological Control SystemsIntroduction, Motivation, and Background

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Publisher
Springer International Publishing
Copyright
© The Author(s) 2014
ISBN
978-3-319-08637-8
Pages
1 –20
DOI
10.1007/978-3-319-08638-5_1
Publisher site
See Chapter on Publisher Site

Abstract

[One can study nonlinear control theory from the point of view of applications, or from a more fundamental point of view, where system structure is a key element. From the practical point of view, questions that arise are often of the form, “How can we...”, for example, “How can we steer a system from point A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A$$\end{document} to point B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B$$\end{document}?” or, “How can we stabilise this unstable equilibrium point?” or, “How can we manoeuvre this vehicle in the most efficient manner?” From a fundamental point of view, the problems are often of a more existential nature, with, “How can we” replaced with, “Can we”. These existential questions are often very difficult to answer in any sort of generality.]

Published: Jul 23, 2014

Keywords: Geometric control theory; Feedback-invariance; Mathematical system theory

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