Generalized Barrier Function–Based Adaptive Sliding Mode Control with Prescribed Error Bounds: Application to Variable Stiffness Actuators

ABSTRACT

This study presents an improved adaptive sliding mode control (ASMC) scheme for uncertain nonlinear systems subject to external disturbances, using a generalized rational barrier function (GRBF). The proposed GRBF extends the conventional rational barrier function (RBF) by introducing a broader class of barrier functions with enhanced error suppression capabilities. A rigorous stability analysis demonstrates that the sliding variable remains confined within a predefined bounded region under the proposed control framework. Furthermore, a specialized case of the generalized function is derived, enabling the sliding variable error to converge to an arbitrarily small residual region. Compared to traditional barrier functions, the GRBF incorporates additional tuning parameters, and a comprehensive sensitivity analysis is performed to evaluate their influence on system behavior. Extensive numerical simulations on a complex multi‐input multi‐output antagonistic variable stiffness actuator (AVSA) system under constant and variable payload demonstrate the superior tracking accuracy of the proposed GRBF‐enhanced ASMC compared to the conventional barrier‐function‐based control approach. Furthermore, a high‐fidelity MATLAB Simscape co‐simulation using a virtual prototype of the actuator is conducted to validate the practical effectiveness of the proposed controller, confirming its robustness and oscillation‐free tracking performance under realistic implementation conditions.