Adaptation of Levant's differentiator based on barrier function. Issue 9 (2nd September 2018)

• Record Type: Journal Article
• Authors: Obeid, Hussein; Fridman, Leonid; Laghrouche, Salah; Harmouche, Mohamed; Golkani, Mohammad Ali
• Is Part Of: International journal of control. Volume 91:Issue 9(2018)
• Page Start: 2019
• Page End: 2027
• Publication Date: 2018-09-02
• Subjects: Levant's differentiator -- sliding-mode control -- adaptive control; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2017.1406149
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: An algorithm for adaptation of Levant's differentiator (LD) gains is designed for the case when the upper bound of second derivative of base signal exists but it is unknown. The barrier function is employed in this algorithm in order to adapt both gains of LD. Thanks to its feature, from the initial time moment it can be guaranteed that the error of estimation of signal belongs to a predefined vicinity of zero. Moreover, the proposed barrier algorithm can ensure the convergence of LD to some vicinity of the first derivative. This barrier adaptation enjoys two main advantages: it ensures a fast convergence and could indicate that LD does not converge in the case of noisy signal.