Prescribed Performance Safety‐Critical Control for Nonlinear Systems With External Disturbance

ABSTRACT This article proposes a novel prescribed performance safety‐critical control tailored for prescribed performance in order to address the trajectory tracking problem of a class of high‐order nonlinear systems with external disturbances. First, a nonrecursive design framework combined with a disturbance observer is introduced to develop a trajectory tracking controller, simplifying the overall control design process. Subsequently, the prescribed performance function (PPF) is integrated with the high‐order control barrier function (HO‐CBF) to transform the tracking error's prescribed performance constraints into safety constraints based control barrier function (CBF), with additional robustness achieved through disturbance compensation based on the observer. This disturbance compensation method constructs robust specified performance safety constraints and robust control Lyapunov functions (RCLF), ensuring the specified performance conditions and system stability, while balancing the tracking control performance and disturbance suppression. Furthermore, a quadratic programming (QP) framework is employed to dynamically adjust the tracking controller within safety constraints and safety constraints to obtain an optimal prescribed performance safety‐critical controller. Finally, the effectiveness of the proposed method is validated through simulations and experiments on a 6‐DOF robotic manipulator with all rotational joints.