Observer‐Based Adaptive Predefined‐Time Nonsingular Terminal Sliding Mode Controller Design and Its Application to Steer‐By‐Wire System

ABSTRACT In this article, a recursive predefined‐time observer‐based adaptive predefined‐time nonsingular terminal sliding mode (RPTO‐APTNTSM) control strategy is proposed for a class of uncertain nonlinear systems. First, a novel PTNTSM controller is designed to guarantee the system tracking error converge to zero in a predefined‐time, where the controller is global non‐singular and the setting time of the control system is independent of the initial states and can be set in advance. Then, a fast nested adaptive law is constructed to update the control gain. With the adaptive method, the adaptive gain can be automatically adjusted with the uncertainty's upper bound, such that not only the system robustness is improved, but also the prior upper bound constraint of the uncertainty is removed. To mitigate chattering caused by undesired large control gain, the RPTO is developed for uncertainty compensation. Therefore, the control gain can be further updated to the upper bound of the uncertainty estimation error, which is much smaller than the uncertainty's upper bound, thereby the chattering is minimized. A detailed Lyapunov stability proof of the proposed strategy is provided. Finally, simulations and experiments on a Steer‐by‐Wire system are conducted to validate the superiority of the control strategy.