New perception error patterns, such as misdetection, emerge in Autonomous Vehicles (AV) and other autonomous systems due to the pervasive implementation of AI-driven algorithms. However, existing planning/control approaches in AVs have not yet adapted to these new error patterns because of their black-box or grey-box nature and high complexity. This lack of adaptation leads to increased collision risk and reduced comfort of passengers. In this paper, the negative effects of the misdetection arising in the AI-enabled perception system are first investigated, where the widely used Intelligent Driver Model (IDM) for the car-following task is selected as a case study. Simulation result shows that the presence of perception errors may lead to unsafe behavior of an IDM. A novel car-following control scheme, Safe IDM, is designed to adapt to misdetection and measurement noise. A state estimation module based on Perception Error Model (PEM) and Intermittent Kalman FIlter (IKF) is designed, and followed by a safety-boundary calculation module on the basis of classical IDM. It is shown that the proposed safe IDM is able to maintain stable following of the leading vehicle in the presence of varying detection rates and measurement noise. Simulation results confirm that, compared to the original IDM that does not consider misdetection errors in its design, the proposed safe IDM exhibits significant improvements in both comfort of passengers and safety. This paper shows that AI-induced perception errors could substantially degrade the performance of autonomous driving functions and increase their collision risk, while the perception-error-aware controller has great potential to reduce their negative effects.