Mathematical systems theory

, Volume 20, Issue 1, pp 193–213 | Cite as

Lie algebraic canonical representations in nonlinear control systems

  • T. Huillet
  • A. Monin
  • G. Salut
Article
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Abstract

This paper is the applied counterpart to previous results [5] for linear-analytic control systems. It is mainly concerned with two canonical representations of the exponential type. They exhibit the Lie algebraic structure of the system in such a form that results on weak controllability are easily derived in an algebraic manner. The first representation is a single exponential of a canonical Lie series in Hall's basis of the Lie algebra of vector fields. The second one is a factorization in terms of simpler exponentials of Hall's basic vectors. Both of them exhibit, as canonical coefficients, an infinite set of characteristic parameters which are a minimal representation of the input paths, when no drift occurs in the system (or, equivalently, in the weak control case). The weak controllability theorem is easily derived from these results, in a purely algebraic way.

Keywords

Basic Vector Algebraic Structure Nonlinear Control Exponential Type Canonical Representation 
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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Copyright information

© Springer-Verlag New York Inc 1987

Authors and Affiliations

  • T. Huillet
    • 1
    • 2
  • A. Monin
    • 1
    • 3
  • G. Salut
    • 1
  1. 1.Laboratoire d'Automatique et d'AnalyseSystèmes du C.N.R.S. (L.A.A.S.)Toulouse CédexFrance
  2. 2.Société Applications Mathématiques et Logiciels (A.M.L.)Rue il-MalmaisonFrance
  3. 3.Compagnie des Signaux et d'Entreprises ElectriquesMontrougeFrance

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