An online evolving framework is proposed to support modeling the safe Automated Vehicle (AV) control system by making the controller able to recognize unexpected situations and react appropriately by choosing a better action. Within the framework, the evolving Finite State Machine (e-FSM), which is an online model able to (1) determine states uniquely as needed, (2) recognize states, and (3) identify state-transitions, is introduced. In this study, the e-FSM’s capabilities are explained and illustrated by simulating a simple car-following scenario. As a vehicle controller, the Intelligent Driver Model (IDM) is implemented, and different sets of IDM parameters are assigned to the following vehicle for simulating various situations (including the collision). While simulating the car-following scenario, the e-FSM recognizes and determines states and identifies the transition matrices by suggested methods. To verify if the e-FSM can recognize and determine states uniquely, we analyze whether the same state is recognized under the identical situation. The difference between probability distributions of predicted and recognized states is measured by the Jensen-Shannon divergence (JSD) method to validate the accuracy of identified transition-matrices. As shown in the results, the Dead-End state which has latent-risks of the collision is uniquely determined and consistently recognized. Also, the probability distributions of the predicted states are significantly similar to the recognized states, declaring that the state-transitions are precisely identified.