Barrier Function-Based Adaptive Integral Sliding Mode Control

In this paper, barrier function-based adaptive discontinuous and continuous integral sliding mode controls are proposed. The main advantage of the proposed algorithms is that they ensure that the solutions of the systems belong to a prescribed vicinity of the desired variables starting from the initial time moment despite of disturbance with unknown upper bound or disturbance with unknown upper bound of its derivative. The proposed algorithms do not require the knowledge of the upper bound of disturbance or its derivative, and, moreover, the control gains are not overestimated.