30 mars 2017 par H. Obeid : Adaptation of Levant’s differentiator based on barrier function.
An algorithm for adaptation of Levant’s differentiator gains is proposed for the case when the upper bound of the second derivative exists but it is unknown. The proposed barrier adaptive algorithm can ensure the convergence of the differentiator to some vicinity of the first derivative. Then, a convergence detection criteria is used to estimate this vicinity. The barrier function is presented to adapt both gains of the differentiator thanks to its feature that can maintain the predefined system’s constraint. The properties of the proposed algorithm and other adaptive Levant’s differentiators in the presence of noise are discussed.