Adaptive Sliding Mode Control for Nonlinear Systems with Uncertainties: A Lyapunov-Based Approach

Abstract

            This study presents a novel adaptive sliding mode control (ASMC) strategy designed to address the challenges posed by nonlinear systems with model uncertainties and external disturbances. The proposed method integrates a Lyapunov-based stability framework with an adaptive law to ensure robust performance, even in the presence of unknown dynamics and bounded perturbations. By employing an adaptive gain adjustment mechanism, the controller eliminates the need for prior knowledge of uncertainty bounds while avoiding the excessive chattering commonly associated with conventional sliding mode control. The stability and convergence of the closed-loop system are rigorously proven using Lyapunov theory, ensuring asymptotic tracking of the desired trajectory. Numerical simulations on benchmark nonlinear systems—including robotic manipulators and chaotic dynamics—demonstrate the superior performance of the proposed approach in terms of rapid convergence, robustness to uncertainties, and minimal control effort. This research contributes to the field of robust control by offering a practically implementable ASMC framework suitable for a wide range of real-world nonlinear systems.