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Local Controllabilifty Along a Reference Trajectory

  • Rosa Maria Bianchini
  • Gianna Stefani
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 83)

Abstract

Let (*) be a C control system defined on a C differential manifold, of the following type
(*)
Sufficient conditions of local controllability along the trajectory t → exp tf0(x0) are aiven. These conditions are conditions on the Lie algebra generated by the vector fields f0, f1,...,fm in x0.

One of the conditions has been proved by Hermes and Sussmann independen-tly under the assumntion f0(x0) = 0.

Keywords

Vector Field Local Controllability Reference Trajectory Analytic Vector Field Nilpotent Associative Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    H. Hermes, “On local and global controllability”, SIAM J. Control Opt. 12 (1974), 252–261.zbMATHMathSciNetGoogle Scholar
  2. [2]
    H. Sussmann, V. Jurdjevic, “Controllability of nonlinear systems”, J. Diff. Ea. 12 (1972), 95–116.Google Scholar
  3. [3]
    J C. Varsan, “On local contre.116bility for non-linear control systems”, Roum. Math. Pures Appl. 29 (1984), 907–919.zbMATHMathSciNetGoogle Scholar
  4. [4]
    H. Hermes, “Control systems which generate decomposable Lie alge-bras”, J. Diff. Eq. 44 (1982), 166–187.Google Scholar
  5. [5]
    H. Sussmann, “Lie brackets and local controllability a sufficient condition for scalar-input systems”, SIAM J. Control and Opt. 21 (1983), 686–713.CrossRefzbMATHMathSciNetGoogle Scholar
  6. [6]
    H. Sussmann, “A general theorem on local controllability”, to ap-pear.Google Scholar
  7. [7]
    N.N. Petrov, “Local controllability of autonomous systems” (in rus-sian) Diff. Uravn. 4 (1968), 1218–1232.Google Scholar
  8. [8]
    P.E. Crouch, C.I. Byrnes, “Local accessibility, local reachability and representations of compact groups”, to appear.Google Scholar
  9. [9]
    R.M. Bianchini, G. Stefani, “Normal local controllability of order one”, Int. J. Control 39 (1984), 701–714.Google Scholar
  10. [10]
    R.M. Bianchini, G. Stefani, “Local controllability and bilineari-zation”, IMA J. Math. Control & Information 1 (1984), 173–183.CrossRefzbMATHGoogle Scholar
  11. [11]
    G. Stefani, “Local controllability of non linear systems: an exam-ple”, System & Control Letters 6 (1985).Google Scholar
  12. [12]
    M. Fliess, “Fonctionelles causales non lineaires et indeterminees non commutatives”, Bull. Soc. Math. France, 109 (1981), 3–40.Google Scholar
  13. [13]
    A.J. Krener, “A generalization of Chow’s theorem and Bang-Bang theorem to non linear control problems”, SIAM J. Control Opt. 12 (1974), 43–52.Google Scholar
  14. [14]
    G. Stefani, “On local controllability of a scalar-input control system”, to appear in MTNS-85 7th Int. Symp. on the Mathematical Theory of Networks and systems, Stockholm 1985 (C. Byrnes, A. Lind-quist, eds.).Google Scholar
  15. [15]
    H. Sussmann, “A general theorem on symmetries and local controlla-bility”, Proceedings of 24th CDC (1985).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1986

Authors and Affiliations

  • Rosa Maria Bianchini
    • 1
  • Gianna Stefani
    • 2
  1. 1.Istituto MatematicoFirenzeItaly
  2. 2.Dip. Sistemi e InformaticaFirenzeItaly

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