Robust Adaptive Fuzzy Control for Second-Order Euler–Lagrange Systems With Uncertainties and Disturbances via Nonlinear Negative-Imaginary Systems Theory

Ensuring robust and precise tracking control in the presence of uncertain multi-input–multi-output (MIMO) system dynamics and environmental variations is a significant challenge in the field of robust and adaptive control theory. While fuzzy control strategies have demonstrated good tracking performance in normal conditions, designing and tuning fuzzy controllers can be a challenging task in highly uncertain environments. In this study, we investigate a novel approach that combines robust nonlinear negative-imaginary (NI) systems theory with a self-adaptive fuzzy control scheme and the Lyapunov synthesis to develop a robust adaptive negative-imaginary-fuzzy (RANIF) control scheme. We optimize the critical parameters of the proposed fuzzy system using a self-tuning technique with a proportional–derivative sliding manifold. Furthermore, unlike the existing adaptive fuzzy control methods, we propose a small number of membership functions and systematically derive the fuzzy rules by employing Lyapunov, nonlinear NI, and dissipativity theories, which simplify the tuning process, work out the matter of “explosion of complexity”, and reduce computational complexity. We demonstrate the global stability of the closed-loop system using nonlinear NI theory. To evaluate the effectiveness of our proposed approach, we present simulation results for two examples involving uncertain MIMO second-order Euler–Lagrange systems. These systems, known for their capacity to represent a diverse range of practical physical systems, serve as suitable testbeds for our methodology. Our results show that RANIF outperforms other control methods, such as nonlinear strictly NI-Fuzzy, fuzzy-logic control, model predictive control, and conventional PID control, in terms of robustness to disturbances and inestimable faults, trajectory tracking performance, and computational complexity.