Effects of Deterministic Measurement Noise on Barrier Function-Based Adaptive Sliding-Mode Control

Abstract

The effect of deterministic measurement noise on barrier function-based adaptive sliding mode controllers (BFASMC) is analyzed. For general bounded deterministic noise signals, it is impossible to select the controller parameters to track some perturbation with unknown bound. Nonetheless, if the assumption of continuity of the noise is added, the tracking of such a perturbation is possible whenever the barrier function width depends on the bound of the noise. If Lipschitz continuity of the noise is assumed, then the barrier function width can be chosen arbitrarily.