High-Order Control Barrier Function-Based Robust Safety-Critical Control With Sampled-Data Input

This article presents an approach to ensure the robust forward invariance of safe sets for sampled-data input nonlinear dynamical systems with model uncertainties. We first design a continuous-time composite controller structure for the uncertain system by integrating an uncertainty compensation term and a state feedback term. The uncertainty compensation term is generated by a nonlinear observer, while the feedback term is subject to linear constraints on a high order control barrier function (HOCBF) which effectively mitigates the adverse effects of the uncertainty observation error on the safety constraints. Then, inspired by the continuous-time controller, a sampled-data controller is proposed where the feedback control term is obtained by solving a new quadratic program (QP) problem with modified HOCBF constraints to address the challenges posed by sampled-data input. Sufficient conditions are derived to guarantee the robust forward invariance of the safe sets for the sampled-data nonlinear dynamical system. From the simulation experiments, it is demonstrated that the proposed method successfully ensures the safety of the sampled-data input dynamical systems with model uncertainties.