An analytical approach to the study of Markov processes is proposed. Using an algorithm for selective search of input–output operators and simple analytical procedures, time probability functions are obtained for real and complex conjugate eigenvalues of the transition intensity matrix. Estimates of the time of onset of the stationary regime are given. Examples of the analysis of homogeneous and heterogeneous Markov processes with piecewise constant transition intensities, non-Markov processes with pseudo-states generated by Erlang flows, as well as substantiation of requirements for the intensity of restoration (efficiency of the repair body) in a technical system are considered. The main results are illustrated by probability estimation in a rigorous analytical form.

An approach to adjusting the parameters of adaptive control in a sliding mode with super-twisting, used for nonlinear systems with parametric uncertainty, is presented. The approach is based on Jaya algorithm, which ensures the efficiency and stability of the control system in changing conditions. Taking into account the complexity of the model description and the presence of uncertainty, as well as fine-tuning the parameters of the regulator in sliding mode with supercooling are essential to ensure optimal system performance. The influence of various system parameters on its behavior and stability is studied using the Jaya algorithm, which ensures the achievement of an optimal mode of operation. The results of numerical simulation show that adaptive control of a nonlinear system in a sliding mode with super-twisting, optimized using the Jaya algorithm, provides higher system performance and resistance to interference, compared with traditional approaches. The effectiveness of the proposed approach is confirmed by the example of an inverted pendulum model on a trolley.

The problem of automating the analysis of handwritten documents is solved. It is shown that artificial neural networks capable of recognizing images after training on the original data set are used to solve such problems. At the same time, the quality of recognizing new images largely depends on the stage of pre-processing of digitized handwritten documents. A particular preprocessing problem is considered - removing cell lines from an image of a notebook sheet. Four methods of image filtering are analyzed using the OpenCV library of the Python language. A neural network of convolutional architecture is trained to recognize handwritten characters. The work of the trained neural network on documents preprocessed by different algorithms is demonstrated.

A self-routing analog-to-digital converter based on a single-layer neural network consisting of basic measuring neurons is considered. For the main measuring neuron, a control system is presented that implements self-routing of signals in a neural network using the “echolocation” method when forming an individual meter of the required bit depth. A method is proposed to reduce the hardware costs of implementing a control system by using a local fragmented control device, the elements of which are distributed among neurons and can be combined to control the operation of an analog-to-digital converter. Functional schemes of a local fragmentary control device with separation of counters used in “echolocation” have been developed, on the basis of which models have been built in the Quartus environment, using the latter to estimate hardware costs measured in the number of LUT logic blocks and registers used. The compilation of the project for a programmable logic integrated circuit showed a 20-25% reduction in hardware costs (depending on the parameters of the neural network), compared with using a control device without separating counters. It should be noted that the local fragmented management device makes it easier to scale the network and increase its fault tolerance.

The features of the use of sacrificial layers in the manufacture of multilayer Al–Ni foil, characterized by the effect of self-expanding high-temperature synthesis, are considered. In order to avoid peeling during the foil production there must be good adhesion between the substrate and the foil. On the other hand, to produce the final product, the foil must be peeled off the surface of the substrate, which implies a low degree of adhesion. It is possible to resolve this technological contradiction by using sacrificial layers, that is, films of material that are applied to the substrate before forming the foil, and then dissolved or etched off, thereby destroying the physical bond between the foil and the substrate. For this reason, it is particularly relevant to study the use of various materials as sacrificial layers in the manufacture of multilayer foils with the effect of self-expanding high-temperature synthesis. A variant of the layout of a magnetron sputtering system is proposed, which makes it possible to use six magnetrons in a single technological cycle for the formation of a multilayer Al–Ni structure. The thickness of the obtained foil is determined using electron microscopy. It is shown that the use of a polyvinyl alcohol film with a thickness of 30 microns as a sacrificial layer makes it possible to peel off multilayer Al–Ni foil without mechanical damage and loss of the ability to react with self-expanding high-temperature synthesis.