Improving trust in the operation of autonomous vehicle (AV) control systems is an actual challenge for overcoming the trough of disillusionment in the development phase. There are identified critical gaps in the field that motivate the development of new theoretically grounded methods: most of the existing methods can be used for specific systems without generality applicability, and the achieved explainability level is aimed only engineers and specialists. This paper aims to provide a user-centered method in order to be able to explain the operation for general users. The research question is: How is it possible to transform complex control systems to approximating systems with explainable operation? In this paper a decision-tree-based solution is proposed that results in a low-order approximating system in explainable form. The application of the method is illustrated through the example of an AV safety detector. The operation of the complex detector is described through decision-tree-based rules that are visualized to explain the original system.