Mathematical modelling of aeronautical environment

On the basis of the study of air flight control, as well as the need to take into account the regional parameters of the airspace, the expediency and the need for mathematical modeling of the air navigation environment were identified. The article deals with the features of the model of air navigation environment, in which the base of the study adopted the basic information used to describe the plan for the execution of air flight. In the study, it was found that in navigation main feature is the geodesic of abstraction, however, such information was found, is not complete for the plan for air flight. The study emphasized the role of taking into account all the restrictions by which certain prohibitions on the use of specific volumes of airspace are imposed. Based on the results obtained, a graph of the geometric representation of the airspace with constraints was constructed. The results of the study allow us to conclude that the construction of a mathematical model of the air navigation environment allows us to achieve the following results: optimization of the distribution of the EAP loads by sectors, visualization of the air navigation situation in the region, the establishment of critical load directions, the collection of data on the load, the study of the factor effects on the regularity and safety of the aircraft movement. The mathematical model of the aeronautical situation was built with the help of a composition of hierarchical type. As a result of such construction of mathematical model its transformation with addition of new models is possible. Using the proposed mathematical model in the framework of discrete event systems can be used to simulate complex air navigation environment with a large number of aircraft. The use of the formalism presented in this study allows a clear distinction between the mechanism of information processing and the information itself in the process of modeling.

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