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Geometry and classification of contact systems : applications to control of nonholomic mechanical systems

Abstract : In the first part of the Ph.D thesis, we characterize all x-flat outputs and their singular loci of any 2-inputs driftless control system wich is equivalent to the chained system. Then we apply that result to the n-trailer system in order to calculate all its x-flats outputs. In the second part, we establish a new model of the n-bar system in (m+1)-dimensional space. With the help of this model, we show that the system is locally equivalent to the m-chained system and also describe its singular locus. Furthermore we analyse its flatness property and determine its minimal flat outputs. In the third part, we give necessary and sufficient conditions for a distribution to be lacally equivalent to the Cartan distribution for surfaces. Finally, in the fourth part, we give necessary and sufficient verifiable conditions for a multi-input affine control system to be orbital feedback linearizable.
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  • HAL Id : tel-00665223, version 1

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Shunjie Li. Geometry and classification of contact systems : applications to control of nonholomic mechanical systems. General Mathematics [math.GM]. INSA de Rouen, 2010. English. ⟨NNT : 2010ISAM0002⟩. ⟨tel-00665223⟩

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