Open AccessUtility of high‐order sliding mode differentiators for dynamical left inversion problems
Author(s) -
Barbot Jean Pierre,
Boutat Driss,
Busawon Krishna
Publication year - 2015
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2014.0124
Subject(s) - differentiator , inversion (geology) , invertible matrix , control theory (sociology) , observer (physics) , mathematics , computer science , dynamical systems theory , control (management) , artificial intelligence , physics , pure mathematics , paleontology , computer network , bandwidth (computing) , structural basin , quantum mechanics , biology
This study highlights some crucial issues related to dynamical left inversion problem for non‐linear systems, that is the recovery of the applied input function from the knowledge of the output and its derivatives. In particular, it is shown that the presence of non‐smooth unknown inputs and non‐involutivity of the forced fields’ distribution constitutes an obstruction to conducting a left inversion. As a solution to this problem, the authors propose a novel left‐invertible form that explicitly considers smooth as well as non‐smooth inputs and for which they design a high‐order sliding mode observer to reconstruct the states and the control inputs. Simulations results are provided to validate the performance of the proposed approach.