Safety-Critical Control for Control Affine Systems under Spatio-Temporal and Input Constraints

Abstract

Safety-critical control is a type of modern control task where potentially conflicting stability, safety, and input constraints coexist. In this paper, the Prescribed-Time Zeroing Control Barrier Function (PT-ZCBF) is introduced, which can be applied as a prescribed-time stability constraint in safety-critical control tasks. Furthermore, we formulate a PT-ZCBF-based Quadratic Program (QP), which is able to mediate the potentially conflicting constraints of safety-critical control. The solution of the newly designed QP, acting as the control input of a safety-critical system, can drive the closed-loop trajectories to converge in a user-defined prescribed time period while observing the safety and input constraints. Finally, we use the Adaptive Cruise Control (ACC) problem as an example of numerical simulation to evaluate the performance of the QP-based method.