Is it Reasonable to Implement Barrier Function Adaptation Under Sensor Noise?

This article studies the behavior of barrier function adaptation (BFA) in the presence of bounded deterministic noises with the known upper bound, both theoretically and experimentally. It is shown that, in the case of discontinuous noises, the predefined performance of the output can be lost. Nevertheless, if the barrier function width (BFW) is selected in accordance to the upper bound of the perturbation, the prescribed performance of the output can be asserted. In the case of continuous noises, BFW needs to be selected at least twice as big as the bound of the measurement noise, i.e., the knowledge of the upper bound of the perturbations is not needed, and the predefined performance of the output is ensured. In the case of Lipschitz continuous noises, BFW can be selected arbitrary, and the system output will be kept in BFW. An experimental study, considering different classes of noises, is designed and implemented on a brushed dc motor to illustrate the conclusions drawn from the theoretical analysis.