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Disturbance Decoupling Via Dynamic Feedback

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Part of the book series: Progress in Systems and Control Theory ((PSCT,volume 8))

Abstract

In the last twenty years there have been extensive studies of geometric methods in control problems. Geometric linear control theory started in the beginning of seventies and is based on the concept of controlled invariant subspaces introduced by Basile and Marro [BM] and by Wonham and Morse [WM]. In the beginning of eighties the nonlinear generalization of the controlled invariant subspace, namely the controlled invariant distribution, was introduced by Isidori et al [IKGM1] and by Hirschorn [H]. This concept has been successfully used in such nonlinear control synthesis problems like disturbance decoupling, noninteracting, invertibility and many others (compare [I] and [NS3]).

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References

  1. G. Basile and G. Marro, Controlled and conditioned invariant subspaces in linear system theory, J. Optimiz. Theory Appl. 3 (1969), 306–315.

    Article  Google Scholar 

  2. J. Descusse and C.H. Moog, Decoupling with dynamic compensation for strong invertible affine nonlinear systems, Int. J. Control, 42 (1985), 1387–1398.

    Article  Google Scholar 

  3. M.D. Di Benedetto, J.W. Grizzle, and C.H. Moog, Rank invariants for nonlinear systems, SIAM J. Control Optimiz., 27 (1989), 658–672.

    Article  Google Scholar 

  4. M. Fliess, A new approach to the noninteracting control problem in nonlinear systems, Proc. 23rd Allerton Conf., Monticello, IL, 1985, 123–129.

    Google Scholar 

  5. M. Fliess, A new approach to the structure at infinity of nonlinear systems, Systems and Contr. Letters, 7 (1986), 419–421.

    Article  Google Scholar 

  6. M. Fliess, A note on the invertibility of nonlinear input-output systems, Systems and Contr. Letters, 8 (1986), 147–151.

    Article  Google Scholar 

  7. M. Fliess, Nonlinear control theory and differential algebra: some illustrative examples, Proc. 10-th IFAC Congress, Munich, 1987.

    Google Scholar 

  8. R.M. Hirschorn, (A,B)-invariant distributions and disturbance decoupling of nonlinear systems, SIAM J. Control Optimiz., 19 (1981), 1–19.

    Article  Google Scholar 

  9. H.J.C. Huijberts, H. Nijmeijer, and L.L.M. van der Wegen, Dynamic disturbance decoupling for nonlinear systems, preprint.

    Google Scholar 

  10. A. Isidori, Nonlinear Control Systems (second edition), Springer, Berlin, 1989.

    Google Scholar 

  11. A. Isidori, A.J. Krener, C. Gori-Giorgi, and S. Monaco, Nonlinear decoupling via feedback: A differential geometric approach, IEEE Trans. Autom. Contr., AC-26 (1981) 331–345.

    Article  Google Scholar 

  12. A. Isidori, A.J. Krener, C. Gori-Giorgi, and S. Monaco, Locally (f,g) invariant distributions, Systems and Contr. Letters, 1 (1981), 12–15.

    Article  Google Scholar 

  13. A. Isidori and C.H. Moog, On the nonlinear equivalents of the notion of transmission zeros, Modelling and Adaptive Control, C.I. Byrnes and A. Kurzhanski (eds.), Lecture Notes in Control and Information Sciences, 105, Springer, Berlin, 1988, 146–158.

    Chapter  Google Scholar 

  14. A.J. Krener, (Ad f,y ), (ad f,g ) and locally (ad f,g ) invariant and controllability distributions, SIAM J. Control and Optimiz., 23 (1985), 523–549.

    Article  Google Scholar 

  15. C.H. Moog, Nonlinear decoupling and structure at infinity, Math. Control, Signals and Systems, 1 (1988), 257–268.

    Article  Google Scholar 

  16. H. Nijmeijer, Control invariance for affine control systems, Int. J. Control, 34 (1981), 824–833, 1981.

    Google Scholar 

  17. H. Nijmeijer and W. Respondek, Dynamic input-output decoupling of nonlinear control systems, IEEE Trans. Automat. Control, AC-33 (1988), 1065–1070.

    Article  Google Scholar 

  18. H. Nijmeijer and A.J. van def Schaft, Controlled invariance for nonlinear systems, IEEE Trans. Automat. Control, AC-27 (1982), 904–914.

    Article  Google Scholar 

  19. H. Nijmeijer and A.J. van def Schaft, The disturbance decoupling problem for nonlinear control systems, IEEE Trans. Automat. Control, AC-28 (1983), 621–623.

    Article  Google Scholar 

  20. H. Nijmeijer and A.J. van der Schaft, Nonlinear Dynamical Control Systems, Springer, New York, (1990).

    Google Scholar 

  21. W. Respondek, Right and Left invertibility of nonlinear Control Systems, Nonlinear Controllability and Optimal Control, H.J. Sussmann (ed.), Marcel Dekker, New York, 1990, 133–176.

    Google Scholar 

  22. W. Respondek and H. Nijmeijer, On local right invertibility of nonlinear control systems, Control-Theory and Advanced Technology, 4 (1988), 325–348.

    Google Scholar 

  23. A.M. Vinogradov, I.C. Krasilshchik, and V.V. Lychagin, Introduction to Geometry of Nonlinear Differential Equations, Nauka, Moscow, 1986, (in russian).

    Google Scholar 

  24. W.M. Wonham and A.S. Morse, Decoupling and pole assignment in linear multivariable systems: A geometric approach, SIAM J. Control and Optimiz., 8 (1970), 1–18.

    Article  Google Scholar 

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© 1991 Birkhäuser Boston

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Respondek, W. (1991). Disturbance Decoupling Via Dynamic Feedback. In: Bonnard, B., Bride, B., Gauthier, JP., Kupka, I. (eds) Analysis of Controlled Dynamical Systems. Progress in Systems and Control Theory, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3214-8_31

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  • DOI: https://doi.org/10.1007/978-1-4612-3214-8_31

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7835-1

  • Online ISBN: 978-1-4612-3214-8

  • eBook Packages: Springer Book Archive

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