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Tautological Control Systems

  • Book
  • © 2014

Overview

Authors:
  1. Andrew D. Lewis

    1. Department of Mathematics and Statistics, Queen's University, Kingston, Canada

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  • Promises a new methodology of study with fundamentally novel tools leading to a radically different way of understanding system structure
  • Eliminates the need to consider control parameterization and the effects of its variation
  • New approach will inspire further work and discussion
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Electrical and Computer Engineering (BRIEFSELECTRIC)

Part of the book sub series: SpringerBriefs in Control, Automation and Robotics (BRIEFSCONTROL)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Introduction, Motivation, and Background

    • Andrew D. Lewis
    Pages 1-20

  3. Topologies for Spaces of Vector Fields

    • Andrew D. Lewis
    Pages 21-30

  4. Time-Varying Vector Fields and Control Systems

    • Andrew D. Lewis
    Pages 31-48

  5. Presheaves and Sheaves of Sets of Vector Fields

    • Andrew D. Lewis
    Pages 49-61

  6. Tautological Control Systems: Definitions and Fundamental Properties

    • Andrew D. Lewis
    Pages 63-95

  7. Étalé Systems

    • Andrew D. Lewis
    Pages 97-106

  8. Ongoing and Future Work

    • Andrew D. Lewis
    Pages 107-118
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Keywords

About this book

This brief presents a description of a new modelling framework for nonlinear/geometric control theory. The framework is intended to be—and shown to be—feedback-invariant. As such, Tautological Control Systems provides a platform for understanding fundamental structural problems in geometric control theory. Part of the novelty of the text stems from the variety of regularity classes, e.g., Lipschitz, finitely differentiable, smooth, real analytic, with which it deals in a comprehensive and unified manner. The treatment of the important real analytic class especially reflects recent work on real analytic topologies by the author. Applied mathematicians interested in nonlinear and geometric control theory will find this brief of interest as a starting point for work in which feedback invariance is important. Graduate students working in control theory may also find Tautological Control Systems to be a stimulating starting point for their research.

Authors and Affiliations

  • Department of Mathematics and Statistics, Queen's University, Kingston, Canada

    Andrew D. Lewis

About the author

Professor Lewis has worked in the areas of geometric mechanics and geometric control theory, lately the latter more so than the former. He is a recognised expert in geometric control theory. He has written many papers on geometric control theory and geometric mechanics, and has supervised five doctoral theses in these areas. He is the author of Geometric Control of Mechanical Systems, published by Springer and dealing with the interface of his two areas of expertise. Together with Manuel de Leon and Juan-Pablo Ortega, Professor Lewis started the Journal of Geometric Mechanics as a venue for publishing research in these areas.

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