Safety Controller Synthesis for Automated Vehicles Systems with Input Saturation

This paper studies the safety control problem of the affine system with input constraints. To address the conflict between the safety and input constraints, a control barrier function (CBF) with a decay parameter is employed to describe the safety condition. Combining this CBF and input constraints, a quadratic program (QP) with an optimal decay rate is established. By analyzing the active and inactive conditions of input constraints and utilizing Karush-Kuhn-Tucker (KKT) method, we can obtain the explicit solution of the established QP. The safety controller based on QP enables the closed-loop system to satisfy the input constraints and guarantees the invariance of safety set. Finally, we validate the effectiveness of the designed safety controller using automated vehicles system with Adaptive Cruise Control (ACC).