Robust Model Reference Adaptive Control With a Full Adaptive Super‐Twisting Sliding Mode Action: Discrete‐Time Stability Analysis and Application

ABSTRACT This work presents a robust model reference adaptive control with a full adaptive super‐twisting sliding mode action (RMRAC‐FASTSM) and its discrete‐time stability analysis using the Lyapunov criterion. The control structure differs from the literature by using a couple of adaptive gains to automatically adjust the weights on the nonlinear and integral components of the STSM action. This strategy alleviates the chattering phenomenon because it reduces the sliding mode action when the system reaches the steady state, improving the closed‐loop system performance and simplifying the controller design process by reducing the number of tuning hyperparameters required during this stage. The proposed control strategy emerges from the union of robust model reference adaptive control and a full adaptive super‐twisting algorithm, resulting in a novel adaptive and robust single‐loop control strategy. The stability analysis provides the controller design constraints, while also demonstrating that tracking error tends to a residual set in the steady state, even when the system is subject to matched and unmatched dynamics. Furthermore, the boundedness of all closed‐loop signals is also proved. The resulting controller is able to control a partially modeled system, where the only required system information is the sign of the high‐frequency gain and the relative degree of the nominal system transfer function. Simulation results corroborate the robustness of the controller dealing with relevant system perturbations and its superiority in relation to other adaptive super‐twisting controllers from the literature.