A fast algorithm for systems decoupling using formal calculus

  • F. Geromel
  • J. Levine
  • P. Willis
Session 16 Nonlinear Systems I
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 63)


The feedback decoupling problem of nonlinear systems is actually well understood in a theoretic point of view. However, to compute the decoupling feedbacks, apart of [9] the only method known by the authors, consists in using a formal derivation program to check if differential expressions are null [3]. We firstly recall the generic interpretation of these expressions in terms of the graph of the system and recall the algorithm of [9] using the minimal length of the paths joining one of the inputs to the ith output. Secondly, we describe the program, and give an application to the control of robot arms.


Minimal Length Characteristic Number Constant Rank Formal Calculus Oriented Path 
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  1. [1]
    D. CLAUDE. Decoupling of nonlinear systems. Syst. and Contr. Letters. Vol.1, no4 (1982), 242–248.Google Scholar
  2. [2]
    D. CLAUDE. Decouplage des systèmes: du linéaire au nonlinéaire, in: Developpement et utilisation d'outils et modèles mathématiques en automatique, analyse des systèmes et traitement du signal. Vol.3, I.D. Landau ed., CNRS, Paris, 1983, 533–555.Google Scholar
  3. [3]
    D. CLAUDE, P. DUFRESNE. An application of Macsyma to nonlinear systems decoupling Lecture Notes in Computer Sciences, Vol.144, Springer, 1982, 294–301.Google Scholar
  4. [4]
    A. ISIDORI, A. KRENER, C. GORI-GIORGI, S. MONACO. Nonlinear decoupling via feedback. IEEE Trans. AC. Vol. AC26, no2 (1981), 331–345.Google Scholar
  5. [5]
    A. ISIDORI. The geometric approach to nonlinear feedback control: a survey. Analysis and Optimization of Systems. Lecture Notes in Control and information sciences no44, Springer, 1982, 517–531.Google Scholar
  6. [6]
    D. SILJAK. On reachability of dynamic systems. Int. J. Syst. Sc. Vol.8, no3, (1977), 321–338.Google Scholar
  7. [7]
    S. NICOSIA, F. NICOLO, D. LENTINI. Dynamical control of industrial robots with elastic and dissipative joints. 8th IFAC World Congress-Kyoto-1981.Google Scholar
  8. [8]
    F. GEROMEL, P. WILLIS. Algorithme de graphe pour le découplage de systèmes nonlinéaires. Option Automatique. Ecole Polytechnique. Promotion 80. Juin 83.Google Scholar
  9. [9]
    A. KASINSKY, J. LEVINE. A fast graph theoretic algorithm for the feedback decoupling problem of nonlinear systems. 8th MTNS conference. Beersheva. June 1983.Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • F. Geromel
    • 1
  • J. Levine
    • 2
  • P. Willis
    • 1
  1. 1.Ecole PolytechniquePalaiseau
  2. 2.Centre d'Automatique et d'Informatique Ecole Nationale Supérieure des Mines de ParisFontaineb LeauFrance

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