Based on a modification of the algorithm for determining the shift vector when forming non-binary Gordon–Mills–Welch sequences (GMWS) in finite fields GF(p^S), where S = mn, an algorithm for determining the shift vector C(m, n, r) = (c₁,c₂, …, c_M) for M summable sequences is developed. This algorithm is based on solving a system of linear equations for the p-adic representation of the parameter r with respect to the shift values of the sequences. It is shown that for a known value of the decimation index vector A(m, n, r) = (d₁,d₂, …, d_M), the number of possible values of the shift vector is L₁ = ((p – 2)!). For given vectors A(m, n, r), the shift vectors C(m, n, r) are given for the formation of GF(5⁴), GF(7⁴), GF(11⁴) GMWS.

For linear descriptor systems subject to inconsistent perturbations, a method is proposed for synthesizing an observer that reconstructs an immeasurable state vector from an output signal available for measurement. When the introduced structural assumptions are fulfilled, the proposed observer also enables restoring the disturbance signal and identifying its unknown parameters. A parameterization method for a certain class of disturbing effects is presented, which makes it possible to move from unknown parameters to linear regression with respect to a certain combination of these parameters. Numerical modeling confirms the operability of the proposed methods.

An interdisciplinary approach to solving problems related to ensuring the stability of unmanned transport systems (UTS) control in a megacity under conditions of geomagnetic and ionospheric disturbances that distort signals from global navigation satellite systems (GNSS) is considered. The approach is based on the combination of Smart City and Industry 4.0 technologies, which creates a synergistic effect and enables the development of reliable solutions. The proposed approach leverages the integration of diverse information into the Smart City ecosystem, obtained through monitoring from a distributed network of dual-frequency GNSS receivers, a distributed network of sensors monitoring geomagnetic activity, and systems monitoring the ionosphere. The data obtained are subject to subsequent analysis using Big Data technologies to predict position errors under conditions of ionospheric and/or geomagnetic disturbances in real time. An adaptive control algorithm for UTS is developed based on a two-step (two-stage) extended Kalman filter. The algorithm dynamically redistributes weights in the system for integrating (merging) heterogeneous data, considering space weather forecasts, thereby increasing the resilience of unmanned aerial vehicle control. The convergence of Smart City and Industry 4.0 technologies creates a synergistic effect, leading to the development of reliable solutions for problems related to ensuring the resilience of UTS control.

The problem of insufficient structuring and documentation of design solutions in the development of software and hardware complexes is considered, especially at the conceptual, architectural, and functional-logical levels. Usually, only certain aspects of the solution are fixed, but it is impossible to imagine it as an independent portable design object. Description tools are proposed to ensure the separation of the invariant logic of the solution from its specific implementation. A generalizing abstraction of an invariant-variable design mechanism is presented, focused on formalizing architectural logic, setting correctness criteria, supporting traceability, and comparing alternative implementations. Based on it, a number of design abstractions are introduced, including interblock adapters, system assistant mechanisms, basic drivers, and local engineering metrics. Abstractions rely on various level representations of computing systems and their design processes.

A mathematical model of the operation of a precision rotary stand with a digital control system and two types of gyroscopes is presented. The wave solidstate and optical gyroscopes are inertial sensing elements of the system. The proposed circuit design implements double integration from measuring sensors of different physical nature. The first type of sensors used are optical angular velocity meters, the operation of which is based on the Sagnac effect laser or fiberoptic gyroscopes. The second type of sensor is a wave solid-state gyroscope, the operating principle of which is based on the Brian effect. The third type of sensor is an optical angular encoder a precision measurement of the rotation angle of the test bench platform. The accuracy and dynamic characteristics of the test bench are evaluated; their provision is based on methods for synthesizing digital controllers in the automatic control system of the test bench.

Assessing the impact of stray light caused by undesirable reflections between the refractive surfaces of lenses is one of the most important stages in the process of designing optical systems that form an image. The stochastic ray tracing methods traditionally used for such an assessment require a huge amount of computation due to the need to trace tens and even hundreds of millions of rays to obtain a highquality image of glare in the plane of the photodetector. Furthermore, calculating glare using stochastic tracing is very timeconsuming, since the number of rays undergoing reflection on the refractive surface is much smaller than the number of refracted rays forming the calculated image. To improve the efficiency of the calculation, an algorithm is proposed based on the deterministic ray tracing method for a glare of a given order, using adaptive interpolation of the coordinates of spurious rays in the image based on the coordinates of these rays as they appear at the entrance pupil of the lens. The essence of the proposed approach lies in reducing the number of traced rays through the use of adaptive interpolation. The application of the proposed algorithm is demonstrated using the example of calculating glare in optical systems of mobile phone lenses. The proposed algorithm is recommended for use in computeraided design systems for optical systems.

A method for calculating the main parameters of an optoelectronic system for monitoring shells the key basic components of largescale products in chemical, oil, and power engineering is presented. A mathematical model of the optical measurement scheme is developed, which makes it possible to analytically define the main parameters of the system determined by the technology used in the production of shells during roll sheetbending machine processing. These parameters make it possible to determine the depth of field of the optical system and the dynamic characteristics of the system. Graphical relationships are obtained that show how the parameters of the optoelectronic control system depend on ovality the main form of deviation from cylindrical shape, which enables reasonable selection of the system parameters for a specific technological process. The obtained dependencies are analyzed, and the possibility of simplifying them for the case of low ovality of the shells are demonstrated. The proposed method is also applicable for controlling cylindrical parts with a different number of faces, which expands the scope of use of the method in automated control systems for sheetbending equipment.

A method for designing optical systems by dividing them into separate groups (frontal, intermediate, and final) with subsequent independent calculation and subsequent coupling, as well as a program for visualizing the initial structure of a projection system for extreme ultraviolet lithography, are presented. The projection system is divided into three groups, and, in accordance with the characteristics of the optical system, the conditions for calculating the structure of each of these groups are determined. The parameters of the mirrors in each group are calculated separately. Then the groups are combined according to the rules for conjugating images and pupils to obtain the initial structure of a mirror optical system without shielding. To visualize the design process, the highlevel programming language MatLab and the optical design software Code V are used to combine the calculation process with the search and selection of a solution. The calculation and search process is intuitively controlled and fast, which makes it possible to obtain a large number of alternative options for initial structures in a short period of time.

A methodology is been proposed that makes it possible to assess the error of various methods for determining volumetric porosity under specified conditions of X-ray examination. The methodology includes a technology for manufacturing a set of samples, scanning them using confocal laser scanning microscopy and the computed tomography method on an X-ray inspection system, as well as assessing the impact of noise using mathematical modeling. The proposed methodology can be used to evaluate and improve the accuracy of measurements on tomograms, as well as to analyze the degradation process of X-ray inspection systems.

Technological solutions for the manufacture of spherical gyroscope rotors cryogenic and electrostatic, with solid and hollow rotors are analyzed. An algorithm is developed containing both standardized and target blocks, enabling the selection of rotor manufacturing process steps. The effectiveness of using fundamentally new technical solutions identified during the research in the algorithm is substantiated.