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Dynamical Polysystems and Control Theory

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Geometric Methods in System Theory

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 3))

Abstract

In these lectures we shall see how it is possible to generalize many results on controllability of linear control systems to the nonlinear ones. A little use of basic definitions of differential geometry is made ; the necessary material used is exposed in appendix.

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Reference

  1. BUSHAW D. (1) “Optimal Discontinuous Forcing Terms” Contribution to the theory of nonlinear oscillations; Vol IV (1958).

    Google Scholar 

  2. “Dynamical Polysystems and Optimisation” Contribution to differential equation 2, p. 351–365

    Google Scholar 

  3. BRUNOVSKY-LOBRY (1) “Bang-Bang, Smooth controllability and perturbation of nonlinear systems” ; to appear.

    Google Scholar 

  4. BROCKETT R.W. (1) “System Theory on Groups Manifolds and Coset Spaces”. SIAM Journal on Control, vol 10, n° 2, (1972) pp. 265–284.

    Article  MathSciNet  MATH  Google Scholar 

  5. ELLIOT D.L. (1) “A Consequence of Controllability” J. of Diff. Equ. 10 (1971), pp. 364–370.

    Article  Google Scholar 

  6. FRANCIS G.K. (1) “The Maximum Principle for Control Distributions”. University of Illinois, Urbana, Illinois ; to appear.

    Google Scholar 

  7. HAYNES-HERMES (1) “Non linear Controllability via Lie Theory”.SIAM Journal on control, vol. 8 (1970) pp. 450–460.

    Article  Google Scholar 

  8. HERMANN R. (1) “On the Accessibility Problem in Control Theory.” Intermat. Symp. on Nonlinear Diff. Equ. and Nonlinear Mech. Academic Press. N.Y. (1963).

    Google Scholar 

  9. HERMES-LA SALLE (1) “Fuctionnal Analysis and Time Optimal Control”. Academic Press, (1969).

    Google Scholar 

  10. JURDJEVIC V. (1) “Certain Controllability Property of Analytic Control Systems”. SIAM Journal on Control vol. 10–2, p. 354–360 (1972)

    Article  MathSciNet  Google Scholar 

  11. JURDJEVIC-SUSSMANN (1) “Controllability of Nonlinear Systems” J. Diff. Equations, 12 (1972) p. 470–476.

    Google Scholar 

  12. KALMAN R.E. (1) “Contribution to the Theory of Optimal Control”. Bol. Soc. Mat. Mex., 5, p. 102–119 (1960).

    MathSciNet  Google Scholar 

  13. KRENER A. (1) “A Generalization of Chow’s Theorem and the Bang Bang theorem to Nonlinear Control Problems”. to appear.

    Google Scholar 

  14. KUCERA. (1) “Solution in large of Control problem : x = (A(l-u) + Bu) x . ” Czech. Math. J. 16 (91), (1966), pp. 600–623.

    MathSciNet  Google Scholar 

  15. KUCERA. (2) “Solution in large of Control Problem : x = (Au + Bv) x . ” Czech. Math. J. IT (92) (1967) pp. 91–96.

    Google Scholar 

  16. LEVINE H. (1) “Singularities of Differentiable Mapping.” Proceeding of Liverpool Singularities Symposium Springer-Verlag Lecture Notes 192.

    Google Scholar 

  17. LOBRY C. (1) “Contrôlabilité des Systèmes Non linéaires”. SIAM Journal on Control vol. 8, n° 4 (1970) pp.573–605.

    Article  MathSciNet  MATH  Google Scholar 

  18. LOBRY C. “Quelques aspects qualitatifs de la théorie de la commande.” These sciences math. Grenoble, mai 1972.

    Google Scholar 

  19. LOBRY C. “Une propriété générique des couples de champs de vecteurs”. Czech. Math, j. 22 (97 / 1972).

    Google Scholar 

  20. LOBRY C. “Controllability of Nonlinear Systems on Compact Manifolds”. to appear in SIAM J. Control.(1973.)

    Google Scholar 

  21. STEFAN (1) “Attainable Sets are Manifolds.” University of Wales. U.C.N.W. Bangai ; to appear.

    Google Scholar 

  22. SUSSMANN H. (1) “Orbits of families of vector fields and integrability of distributions”. to appear in Trans. Amer. Math. Soc.

    Google Scholar 

  23. THOM (1) “Les singularités des applications différentielles”. Annales de I’Institut Fourier, VI, (1956) p. 43–87.

    Article  MathSciNet  Google Scholar 

  24. WEISS (1) “Controllability and Observability”. Lecture Notes, Summer School, CIME (1968).

    Google Scholar 

General references

  • LEE-MARKUS (1) “Foundations of Optimal Control Theory” John Wiley and Sons, Inc. New-York, London Sidney (1967).

    Google Scholar 

  • CHEVALLEY C. (1) “Theory of Lie groups”. Princeton University Press, Princeton New Jersey, (1946).

    MATH  Google Scholar 

  • BISHOP-CRITTENDEN (1) “Geometry of Manifolds”. Academic Press, New York, (1964).

    Google Scholar 

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Author information

Authors and Affiliations

  1. U.E.R. Mathématiques et Informatique, Université Bordeaux I, 351, cours de la Libération, Talence, France

    C. Lobry

Authors
  1. C. Lobry
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Editor information

D. Q. Mayne R. W. Brockett

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© 1973 D. Reidel Publishing Company, Dordrecht

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Lobry, C. (1973). Dynamical Polysystems and Control Theory. In: Mayne, D.Q., Brockett, R.W. (eds) Geometric Methods in System Theory. NATO Advanced Study Institutes Series, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2675-8_1

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  • DOI: https://doi.org/10.1007/978-94-010-2675-8_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-2677-2

  • Online ISBN: 978-94-010-2675-8

  • eBook Packages: Springer Book Archive

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