GENERAL THEOREM ON LOCAL CONTROLLABILITY.

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Abstract

We prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point. Our result shows that many known sufficient conditions can be derived in a unified way from a single general principle, namely, the combination of a nilpotent approximation with the use of input symmetries. A number of new sufficient conditions are obtained. All these results follow from one simple general principle, namely, that local controllability follows whenever brackets with certain symmetries can be 'neutralized,' in a suitable way, by writing them as linear combinations of brackets of a lower degree. Both the class of symmetries and the definition of 'degree' can be chosen to suit the problem.

Original languageEnglish (US)
Pages (from-to)158-194
Number of pages37
JournalSIAM Journal on Control and Optimization
Volume25
Issue number1
DOIs
StatePublished - Jan 1 1987

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All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

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