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Geometric Methods in System Theory

Proceedings of the NATO Advanced Study Institute held at London, England, August 27-September 7, 1973

  • Conference proceedings
  • © 1973

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Editors:
  1. D. Q. Mayne
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  2. R. W. Brockett
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Part of the book series: Nato Science Series C: (ASIC, volume 3)

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Table of contents (21 papers)

  1. Front Matter

    Pages I-VII
    Download chapter PDF

  2. Dynamical Polysystems and Control Theory

    • C. Lobry
    Pages 1-42

  3. Lie Algebras and Lie Groups in Control Theory

    • Roger W. Brockett
    Pages 43-82

  4. Realization Theory of Bilinear Systems

    • Alberto Isidori, Antonio Ruberti
    Pages 83-130

  5. An Introduction to Stochastic Differential Equations on Manifolds

    • J. M. C. Clark
    Pages 131-149

  6. General Theory of Global Differential Dynamics

    • Lawrence Markus
    Pages 150-158

  7. Two Proofs of Chow’s Theorem

    • P. Stefan
    Pages 159-164

  8. On Necessary and Sufficient Conditions for Local Controllability Along a Reference Trajectory

    • Henry Hermes
    Pages 165-173

  9. The High Order Maximal Principle

    • Arthur J. Krener
    Pages 174-184

  10. Optimal Control on Manifolds

    • M. L. J. Hautus
    Pages 185-193

  11. Problems in Geodesic Control

    • John Grote
    Pages 194-204

  12. Controllability in Nonlinear Systems

    • Ronald M. Hirschorn
    Pages 205-214

  13. Control Theory in Transformation Semigroups

    • Gerald S. Goodman
    Pages 215-226

  14. The Imbedding Problem for Finite Markov Chains

    • Søren Johansen
    Pages 227-236

  15. Some remarks on the geometry of systems

    • Robert Hermann
    Pages 237-242

  16. Minimal Realizations of Nonlinear Systems

    • Héctor J. Sussmann
    Pages 243-252

  17. Causal Dynamical Systems: Irreducible Realizations

    • Velimir Jurdjevic
    Pages 253-262

  18. On the Internal Structure of Bilinear Input-Output Maps

    • E. Fornasini, G. Marchesini
    Pages 263-274

  19. Optimal Control of Discrete Bilinear Systems

    • K. N. Swamy, T. J. Tarn
    Pages 275-284

  20. Diffusions on Manifolds Arising from Controllable Systems

    • David L. Elliott
    Pages 285-294
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Keywords

About this book

Geometric Methods in System Theory In automatic control there are a large number of applications of a fairly simple type for which the motion of the state variables is not free to evolve in a vector space but rather must satisfy some constraints. Examples are numerous; in a switched, lossless electrical network energy is conserved and the state evolves on an ellipsoid surface defined by x'Qx equals a constant; in the control of finite state, continuous time, Markov processes the state evolves on the set x'x = 1, xi ~ O. The control of rigid body motions and trajectory control leads to problems of this type. There has been under way now for some time an effort to build up enough control theory to enable one to treat these problems in a more or less routine way. It is important to emphasise that the ordinary vector space-linear theory often gives the wrong insight and thus should not be relied upon.

Bibliographic Information

  • Book Title: Geometric Methods in System Theory

  • Book Subtitle: Proceedings of the NATO Advanced Study Institute held at London, England, August 27-September 7, 1973

  • Editors: D. Q. Mayne, R. W. Brockett

  • Series Title: Nato Science Series C:

  • DOI: https://doi.org/10.1007/978-94-010-2675-8

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1973

  • Hardcover ISBN: 978-90-277-0415-3Due: 31 December 1973

  • Softcover ISBN: 978-94-010-2677-2Published: 01 June 2012

  • eBook ISBN: 978-94-010-2675-8Published: 06 December 2012

  • Series ISSN: 1389-2185

  • Edition Number: 1

  • Number of Pages: VII, 314

  • Topics: Systems Theory, Control, Algebraic Geometry

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