Today, in the digital age, the problem of pattern recognition is very relevant. In particular, the task of text recognition is important in banking, for the automatic reading of documents and their control; in video control systems, for example, to identify the license plate of a car that violated traffic rules; in security systems, for example, to check banknotes at an ATM and in many other areas. A large number of methods are known for solving the problem of pattern recognition, but the main advantage of neural networks over other methods is their learning ability. It is this feature that makes neural networks attractive to study. The article proposes a basic neural network model. The main algorithms are considered and a programming model is implemented in the Python programming language. In the course of research, the following shortcomings of the basic model were revealed: low learning rate (the number of correctly recognized digits in the first epochs of learning); retraining - the network has not learned to generalize the knowledge gained; low probability of recognition - 95.13%.To solve the above disadvantages, various techniques were used that increase the accuracy and speed of work, as well as reduce the effect of network retraining.

Recently, unmanned aerial vehicles have been an important part of scientific research in various fields. Quadrocopter is an unmanned aerial vehicle with four rotors, two of which rotate clockwise, the other two counterclockwise. Changing the speed of screw rotation allows you to control the movement of the apparatus. The article proposed and tested a mathematical model of a quadcopter. They presented the development of a simple control algorithm that allows to stabilize the height and angular position. The research results show the efficiency of the algorithm and the possibility of its practical implementation. The developed mathematical model can be used instead of a real quadcopter, which will significantly reduce the time during research, as well as avoid the quadrocopter damage, reducing the number of launches.

Managing the systems which behaviour is non-deterministic is one of the most important problems in modern management theory. Today, systems with structural and behavioural complexity are prevalent in all areas of human activity, and therefore, their research is of the utmost importance. Such systems, as opposed to deterministic systems, are called non-deterministic. They are characterised by difficult predictable behaviour determined both by external random influences, and within the systems themselves. A clear example of a non-deterministic system is crowds of people, factories, and computer networks and systems. The problem of non-deterministic behaviour directly within the context of professional activities can be seen using an example of building syntactic analysers. The aim of the paper is to design a class of systems oriented towards supporting elements of a discrete event model. The target of research is to simulate discrete event models. The subject of research is a creation of a discrete event model based on the behaviour of an undetermined finite state automaton. During the preparation of the paper, there was developed and practically implemented an algorithm for the application, which materializes the principle of working with threads. The results obtained in the paper are aimed at solving the problem of parallel data processing based on the parallelism of NFA's (non-deterministic finite automaton) behaviour when reading the input string characters. As a result, this should have a positive impact on the regulation of the simulation processes of a non-deterministic system, increasing its efficiency and stability. In conclusion, the algorithm of the application work is disclosed and conclusions about the effectiveness and efficiency of its development are drawn.