Adaptation of Levant's differentiator based on barrier function

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.