Adaptive gain sliding mode control for uncertain nonlinear systems using barrier-like functions

Abstract Uncertain nonlinear systems often face challenges such as unmodeled dynamics and disturbances, which can degrade control performance and robustness. Traditional sliding mode controllers with constant gains may suffer from excessive chattering or fixed response rates, while existing adaptive methods often entail intricate theoretical analysis or mathematical computations. To address these limitations, this paper proposes a novel adaptive gain sliding mode controller (AGSMC) that integrates a barrier-like function (BLF) with a BLF-based disturbance observer for a class of uncertain nonlinear systems. The BLF is first defined and applied to design the control gain, while the BLF-based disturbance observer dynamically updates this gain to relax the need for prior knowledge of disturbance bounds. Compared to the constant-gain sliding mode control, the proposed AGSMC enhances response speed, robustness, and significantly reduces chattering in the control law during the sliding phase. The system's stability under the AGSMC framework is rigorously proved by the Lyapunov stability theorem. Numerical simulations demonstrate the effectiveness of the proposed method, showing superior performance over the traditional sliding mode controller and two other adaptive sliding mode controllers.