Geodesic
Tracking through singularities using sliding mode differentiators
Kybernetika, Tome 51 (2015) no. 1, pp. 20-35.

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In this work, an alternative solution to the tracking problem for a SISO nonlinear dynamical system exhibiting points of singularity is given. An inversion-based controller is synthesized using the Fliess generalized observability canonical form associated to the system. This form depends on the input and its derivatives. For this purpose, a robust exact differentiator is used for estimating the control derivatives signals with the aim of defining a control law depending on such control derivative estimates and on the system state variables. This control law is such that, when applied to the system, bounded tracking error near the singularities is guaranteed.
DOI : 10.14736/kyb-2015-1-0020
Classification : 41A30, 93B12, 93C10
Keywords: singularities; sliding mode differentiator; tracking 
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Castillo-Toledo, Bernardino; Di Gennaro, Stefano; López-Cuevas, Armando. Tracking through singularities using sliding mode differentiators. Kybernetika, Tome 51 (2015) no. 1, pp. 20-35. doi : 10.14736/kyb-2015-1-0020. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-1-0020/

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