A new mathematical model of the intelligent access monitoring and control system based on the cybernetic approach is proposed for solving the problems of vehicle access to the territory of an organization. The distinctive feature of the mathematical model is the ability to take into account and recognize normal and abnormal situations at the protected object and develop control actions. To localize vehicles and recognize their license plates, the composition of traditional methods of image processing and two-pass classification performed by the developed modified architecture of convolutional neural network MobileNet is offered. The composition allows to define additional identification features of the object. The proposed adaptations allow to recognize the situation in real time with low computational costs and high accuracy. The natural experiment has shown that the integration of the modern hardware means and algorithms of object detection and recognition, even in the rough conditions of street closed-circuit television monitoring, provides not less than 96% accuracy, and the processing time of one frame is not more than 0.094 s based on the Nvidia GeForce 1080Ti graphic processor. High recognition accuracy without loss of speed in the real-time mode is achieved by integrating the modern hardware means and the algorithms of object detection and recognition. The program module in Python using the Tensorflow and Keras library is developed for carrying out the access control functions.