The purpose of this research is to develop a device capable of compensating for laser beam positioning error during processing of workpieces. This research is relevant, since several errors occur when processing workpieces with a laser beam, which lead to decrease in the level of accuracy. Two factors lead to these errors, such as the presence of vibrations and unstable beam waist position of the laser beam. It is known that one of the main reasons of unstable beam waist position of the laser beam is uneven surface of the workpiece. When processing a workpiece with a laser beam, the uneven surface of the workpiece causes the beam waist position to change. The position of the beam waist is important because it affects the accuracy of the workpiece. In order to reduce errors in the positioning of the beam waist, a system or mechanism is needed that can compensate for these errors. To achieve this, the system or mechanism must have ability to adapt to the surface of the workpiece. Thus, the development of the device in this study is a solution to the problem that arises during laser processing. In this research, an adaptive laser beam head device is designed which has adaptive capabilities to the surface of the workpiece so that it can compensate for position errors, stabilize the beam waist position, and reduce internal vibrations during workpiece processing. The laser beam head in this research can move in 3 degrees of freedom. With this ability, the laser beam head can move to follow the surface shape and adjust the beam waist position to the workpieces. During operation, to be able to track the position of the laser beam on the workpiece, the device is equipped with a camera. In this research, an experiment with mockup of this device was conducted to determine the level of its capabilities. From the experiment, it can be concluded that device is performing its objectives successfully. It can maintain the position of the laser beam waist on the surface of workpiece with a relatively high level of accuracy. This is evidence by the relatively low error rate. In general, this device can be used and implemented as a system for compensating the positioning error of the laser beam during workpiece processing and also can be implemented to improve the technology of workpiece processing with a high level of accuracy.

We carried out the development and study of methods for changing the sensitivity of Fiber Bragg Gratings (FBG) to temperature and strain by applying various low-melting metals. Investigation of sensitive elements based on SMF-28 single-mode optical fibers with formed FBG and various metal coatings applied over the fiber have been made. The influence of FBG coating with low-melting metals on its sensitivity to temperature and deformation has been studied. Various fiber-optic sensitive elements have been developed, which are fibers with fiber Bragg gratings formed in them, while coatings of various thicknesses of tin or solder in the form of an alloy of tin and lead (Sn63Pb37) were deposited on the area with such diffraction structures. The presented experimental data are in good agreement with the calculated ones. The temperature sensitivity of the Bragg grating resonance with a solder or tin coatings is 4 times higher than the sensitivity of an uncoated grating. In turn, the analysis of the sensitivity to stretching allows us to conclude that, in comparison with the standard FBG, the sensitivity of the grating in the coating decreases and is about 0.017 pm/(µm/m) compared to 1.2 pm/(µm/m) (for the wavelength of the Bragg resonance 1530 nm) for a standard FBG without coating. The results obtained can be used to control and change the FBG sensitivity to temperature and/or deformation, depending on the conditions of the problem being solved in the field of creating fiber-optic measuring devices.

One of the applications of polarization maintaining (PM) fibers is the creation of various sensors including level and hydrostatic pressure sensors. An external mechanical stress on a PM fiber causes cross-polarization coupling. In micro- and macro-bend pressure sensors, the attenuation of the optical signal increases with increasing external pressure. Combination of two physical principles in one sensor allows to create fiber-optic sensors of high sensitivity for operation at pressure more than 18 kPa. At the same time, the registration scheme is significantly simplified. An optical fiber with an elliptical ESC-4 stress cladding was used as a prototype. A superluminiscent diode ThorLabs S5FC1005SXL with a center wavelength of 1560 nm and a spectrum half-width of 45 nm was used in the study. In this work, the effect of induced periodic mechanical stress on cross-polarization coupling magnitude in a PM fiber with an elliptical stress cladding was considered. The induced periodic stress was generated by a proposed and specially fabricated periodic structure of optical fiber sections bonded to a glass substrate. The pressure on the fiber prototype was changed by weights of known mass as well as by rotating the fiber around its axis with a step of 5°. Hydrostatic pressure was created by means of a water tank placed in the barocamera. The cross-polarization coupled power was recorded with two photodetectors using a polarization beam splitter. It is shown that the largest value of the relative coupled power is achieved at the period of mechanical stress equal to the beat length of PM fiber. The dependence of the relative coupled power on the hydrostatic pressure is obtained for the prototype sensor. It is shown that the highest value of the relative coupled power is achieved at a pressure of 80 kPa. The threshold sensitivity amounted to 20 kPa. The decrease in coupled power at pressures greater than 80 kPa is attributed to induced optical losses. At pressure less than 20 kPa, a hysteresis of indicators up to 0.006 relative units is noticeable. A sample sensor for measuring hydrostatic pressure up to 80 kPa with the standard deviation of measurement results up to 7 % was obtained. The threshold sensitivity is limited to 20 kPa. The performed research can be applied in the development of fiber-optic pressure sensors.

A wide class of smooth continuous dynamic nonlinear systems (control objects) with a measurable state vector is considered. The problem of finding a special function (Lyapunov function), which guarantees asymptotic stability for the presented class of nonlinear systems in the framework of the second Lyapunov method, is posed. It is known that the search for the Lyapunov function is an extremely difficult problem that has no universal solution in stability theory. The methods of selection or search of the Lyapunov function for stability analysis of closed linear stationary systems and for nonlinear objects with explicitly expressed linear dynamical and nonlinear static parts are well studied. At the same time, no universal approaches to finding the Lyapunov function for a more general class of nonlinear systems have been identified. In this paper, we propose a new approach to the search of the Lyapunov function for analyzing the stability of smooth continuous dynamic nonlinear systems with a measurable state vector. The essence of the proposed approach consists in the representation of some function through the sum of nonlinear summands representing the elements of the object state vector multiplied by unknown coefficients. The search for these coefficients is performed using a classical genetic algorithm including mutation, selection, and crossover operations. The found coefficients provide all the necessary conditions for the Lyapunov function (within the framework of the second Lyapunov method). The genetic algorithm approach does not require a training sample which imposes restrictions in the form of the structure of control objects included in it. A new method for finding the Lyapunov function represented as a nonlinear series with known functions multiplied by unknown coefficients is proposed. The effectiveness of the proposed method is demonstrated using computer simulations with a fixed number of iterations and varying population size. The dependence of the number of successfully found Lyapunov functions on the number of iterations of the genetic algorithm has been established. The convergence of the genetic algorithm using Holland’s schemes is analyzed. It is shown that the values of the sought coefficients of the potential Lyapunov function, at each algorithm iteration, approach the coefficients of the Lyapunov function which was also represented as a Taylor series. The method proposed in this paper outperforms known analogs in terms of speed, considers the decomposition of the potential Lyapunov function into a Taylor series with unknown coefficients, instead of using counterexamples or template functions.

In the paper, the problem of compensation of external disturbance in multichannel systems with unmeasurable state vector and delay in the control channel is considered. It is assumed that the disturbance has a harmonic form. To solve the problem of estimating the state vector of a system, a full-order observer with Unknown Input Observer is constructed. A new observer of external disturbance is formed on the basis of the state vector estimates produced by this observer. As a result, a system is formed that uses estimates with an extended state vector. For this system, a regulator is constructed that provides compensation of the disturbance. The proposed algorithm guarantees boundedness of all signals in the closed-loop system and asymptotic stability of the output. It does not require identification of parameters of external disturbance. To demonstrate the performance and efficiency of the proposed approach, computer simulation using MATLAB Simulink software environment is performed. The developed algorithm can be effectively applied in systems with external disturbance in the form of sinusoidal signals, including systems exposed to wind, ship systems, motion control systems of robotic complexes of various types, and others.

This paper studies the trajectory tracking problem and the controller gain adjustment problem for Wheeled Mobile Robots. The controller gain has a great influence on the robot’s trajectory tracking: it can influence both the tracking accuracy and the tracking speed. Therefore, it is very important to choose a suitable control gain during the controller design process. Current neural network gain controllers have a complex structure and require a lot of calculations to find the optimal value. To solve this problem, we design a trajectory tracking controller with a simple structure with adaptive gain by combining the controller with a neural network. The input to this controller is the robot’s attitude error. The controller has no hidden layer and directly outputs the trajectory tracking control law. Firstly, the kinematic controller is designed based on Lyapunov function method to ensure that the robot moves according to the reference trajectory. Then, the online gain adjustment algorithm is designed by using neural network to realize the fast adjustment of the controller gain and ensure the reliability of the controller. Finally, the backstepping method is utilized to design the velocity tracking controller based on the error between the virtual velocity and the actual velocity. Considering the influence of the external environment, we also design a nonlinear disturbance observer to estimate the total disturbance on the robot. We perform simulation experiment in MATLAB. The result of the experiment shows that the control algorithm proposed in this paper can realize the accurate tracking of the robot on the specified trajectory. The gain adjustment algorithm we designed can find the optimal gain value quickly and efficiently, thus improving the stability and efficiency of the controller. The method can be applied to most mobile robot trajectory tracking problems and solves the problem of control gain adjustment.

The work is devoted to the study of the characteristics of the state control of a thin-film element based on a phase-change GeTe material. The properties of such an element have been controlled by the action of sequences of ultrashort laser pulses. This action leads to a rapid heating of the thin film element and provides a phase transition between states with a resistance different by several orders of magnitude. The dynamics of the resistance was studied using a high speed oscilloscope according to the scheme where the element under study was the voltage divider arm of a highly stable source. Three different types of conductivity switching were observed for 100 nm thin films. For low energy laser radiation, several distinct states were obtained in which the material film has predominantly semiconducting properties. As the energy of the optical pulses increases, the number of possible stable states determined by the specific conductivity of the material decreases to two, one of which (low resistance) is exclusively metallic properties. In all cases, the time taken to switch to a stable state does not exceed a few tens of nanoseconds for films up to 100 nm thick. The study has demonstrated that the structures described can be used to implement optically controlled memristive elements. In addition, the large number of possible allowable specific resistances of the element will make it possible to use it to increase the information capacity of memory cells based on phase-change materials or to implement optoelectronic neuromorphic systems.

We have studied the optical and luminescence properties at room temperature of ultrathin colloidal semiconductor cadmium selenide nanoscrolls with a thickness of 2.5 monolayers. For colloidal synthesis of the objects under study, cadmium acetate dihydrate Cd(CH3COO)2·2H2O and trioctylphosphine selenide were used as precursors of cadmium and selenium, respectively, and solutions of oleic acid and octadecene were also used. Luminescence spectrum of cadmium selenide nanoscrolls was recorded using a fiber charge coupled device spectrometer. Spectrally resolved photoluminescence decays for nanoparticles were measured with the use of time-correlated single photon counting technique. The emission of the cadmium selenide nanoscrolls consists of interband and recombination luminescence bands. We found that the normalized photon numbers of recombination luminescence are larger than the normalized photon numbers of interband luminescence. We determined dominant wavelengths, chromaticity coordinates, and correlated color temperatures of ultrathin colloidal semiconductor cadmium selenide nanoscrolls. These ultrathin cadmium selenide nanoscrolls are promising for application in light-emitting diodes.

The problem of optimizing the choice of parameters for installing a video camera, such as the location and viewing angles, tilt and pan to increase the information content of the generated video signal, is considered. The relevance of the paper is due to the lack of methods and programs for automating the process of choosing these parameters. The problem is solved when the pixel density is reached, which is necessary for solving the task of observation. It is based on the proposed model for representing view areas, surveillance and camera locations as discrete sets in accordance with the observation task being solved, which determines the required minimum pixel density as well as selected criteria and restrictions. It gives the opportunity to solve the problem programmatically, unlike existing solutions that use empirical approaches. The main and additional criteria as well as limitations are formulated according to which it is possible to optimize the position of the camera relative to the required surveillance area — the observation task to be solved, the minimum required camera resolution and the maximum information content of the generated image. Algorithms for calculating estimates of the near, far and side boundaries of the view area as well as view angles, pan and tilt are formulated. The adequacy of the proposed model to real areas of observation, review and location of cameras is substantiated. An example of solving an optimization problem is given, which confirms the correctness of using the proposed method. The results obtained make it possible to automate the design process and minimize the influence of the human factor when choosing the location and installation parameters of cameras in the process of designing surveillance systems. The results of the work can be used in the development of algorithms and programs for computer-aided design of surveillance systems.

Generating a realistic three-dimensional model of the human body is a very time-consuming task. Even with the necessary computing resources, generation errors occur on the figures of people who differ from the average physique. In this paper, an experimental algorithm for reading anthropometric data from only two full-face and profile photographs is proposed. The proposed solution to the problem of generation using the selection of anthropometric points involves setting the constraints of the SMPL (Skinned Multi-Person Linear Model) model. For segmentation of the human body based on empirical studies, a modification of the Fully Connected Convolutional Neural Network (FCN) ResNet101, trained on the COCO Segmentation 2017 dataset, was used. With its help, the basis for the detection of anthropometric points in full-face and profile photos was obtained. The error in determining anthropometric points ranges from 2 to 5 % depending on their location. The constraints for the SMPL rendering model are calculated using the Levenberg- Marquardt algorithm. For its correct operation, a special cost function is proposed, taking into account the features of this task. The dataset collected by the authors of the article (117 people of different physiques and height) shows that the proposed method allows you to obtain a small average absolute error (MAE = 0.0395 m) and a high coefficient of determination (R2 = 0.913). The graph of anthropometric points sets stricter conditions for generating a figure and any deviation from the graph is a consequence of a large generation error. The proposed solution allows you to accurately generate a model of the human body. At the same time, low requirements for computing resources and the quality of users’ initial photos remain. The proposed solution can be used in online fitting rooms, which adds additional complexity to the task due to the requirements to restore the figure from only two pictures as well as the need to accurately reproduce the features of male and female figures.

At present, the interpretability of Natural Language Processing (NLP) models is unsatisfactory due to the imperfection of the scientific and methodological apparatus for describing the functioning of both individual elements and models as a whole. One of the problems associated with poor interpretability is the low reliability of the functioning of neural networks that process natural language texts. Small perturbations in text data are known to affect the stability of neural networks. The paper presents a method for testing NLP models for the threat of evasion attacks. The method includes the following text adversarial examples generations: random text modification and modification generation network. Random text modification is made using homoglyphs, rearranging text, adding invisible characters and removing characters randomly. The modification generation network is based on a generative adversarial architecture of neural networks. The conducted experiments demonstrated the effectiveness of the testing method based on the network for generating text adversarial examples. The advantage of the developed method is, firstly, in the possibility of generating more natural and diverse adversarial examples, which have less restrictions, and, secondly, that multiple requests to the model under test are not required. This may be applicable in more complex test scenarios where interaction with the model is limited. The experiments showed that the developed method allowed achieving a relatively better balance of effectiveness and stealth of textual adversarial examples (e.g. GigaChat and YaGPT models tested). The results of the work showed the need to test for defects and vulnerabilities that can be exploited by attackers in order to reduce the quality of the functioning of NLP models. This indicates a lot of potential in terms of ensuring the reliability of machine learning models. A promising direction is the problem of restoring the level of security (confidentiality, availability and integrity) of NLP models.

Motion estimation plays a crucial role in video coding; the Adaptive Rood Pattern Search (ARPS) algorithm is a well known fast motion estimation algorithm. However, ARPS has certain limitations, such as the lack of an accurate starting motion vector, a fixed Zero Motion Prejudgment (ZMP) threshold unsuitable for fast motion video sequences, and the repetitive use of a Unit Rood Pattern (URP) resulting in increased computational complexity. To address these issues, this paper proposes a novel algorithm called Efficient Adaptive Rood Pattern Search (EARPS). EARPS overcomes these limitations by employing the Full Search algorithm to obtain optimal motion vectors for the first column in each frame, adopting a dynamic ZMP threshold that adapts to varying motion speeds in video sequences and utilizing URP only once to reduce computational overhead. The performance of the new proposed EARPS algorithm is evaluated and compared with that of ARPS algorithm using various video sequences with different motion speeds. The number of searching points and Peak Signal-to-Noise Ratio (PSNR) are used to quantify computing complexity and accuracy. The experimental findings show that EARPS surpasses ARPS in terms of computing complexity while retaining a decent degree of PSNR accuracy. The proposed EARPS motion estimation algorithm main contribution is to achieve high speed with reasonable accuracy, regardless of the type of motion speed in the video frames. The EARPS algorithm offers a substantial advancement over ARPS, delivering a more efficient motion estimation method with broader applicability in video processing. It represents a significant contribution to the development of effective motion estimation algorithms.

In the modern world, the widespread use of information and communication technology has led to the accumulation of vast and diverse quantities of data, commonly known as Big Data. This necessitates the need for novel concepts and analytical techniques to help individuals extract meaningful insights from rapidly increasing volumes of digital data. Clustering is a fundamental approach used in data mining to retrieve valuable information. Although a wide range of clustering methods have been described and implemented in various fields, the sheer variety complicates the task of keeping up with the latest advancements in the field. This research aims to provide a comprehensive evaluation of the clustering algorithms developed for Big Data highlighting their various features. The study also conducts empirical evaluations on six large datasets, using several validity metrics and computing time to assess the performance of the clustering methods under consideration.

Despite the widespread use of automatic speech recognition and video subtitles, sign language is still a significant communication channel for people with hearing impairments. An important task in the process of automatic recognition of sign language is the segmentation of video into fragments corresponding to individual words. In contrast to the known methods of segmentation of sign language words, the paper proposes an approach that does not require the use of sensors (accelerometers). To segment the video into words in this study, an assessment of the dynamics of the image is used, and the boundary between words is determined using a threshold value. Since in addition to the speaker, there may be other moving objects in the frame that create noise, the dynamics in the work is estimated by the average change from frame to frame of the Euclidean distance between the coordinate characteristics of the hand, forearm, eyes and mouth. The calculation of the coordinate characteristics of the hands and head is carried out using the MediaPipe library. The developed algorithm was tested for the Vietnamese sign language on an open set of 4364 videos collected at the Vietnamese Sign Language Training Center, and demonstrated accuracy comparable to manual segmentation of video by an operator and low resource consumption, which will allow using the algorithm for automatic gesture recognition in real time. The experiments have shown that the task of segmentation of sign language, unlike the known methods, can be effectively solved without the use of sensors. Like other methods of gesture segmentation, the proposed algorithm does not work satisfactorily at a high speed of sign language when words overlap each other. This problem is the subject of further research. 

Solving the problem of predicting the immune response against foreign protein sequence fragments processed by cells is one of the major milestones on the road to the personalized cancer vaccine development. The selection of peptides participating in the immune response is a complex multi-stage process of filtering initial sequences to present their fragments on the cell surface. The most studied task regarding this filtering nowadays is the prediction of the binding probability of peptides to major histocompatibility complex molecules. Modern methods for predicting this stage are usually based on algorithms using artificial neural networks, which make it impossible to interpret the result predictions of such models. One of the methods to overcome this limitation is the use of interpretable hidden Markov models. In this work, an analysis of the binding prediction task is performed. As a result, a method for constructing interpretable models that consider domain-specific constraints and requirements is proposed. A method for the constriction, training and interpretation of hidden Markov models was proposed for each class of molecules. The construction and training are based on maintaining the model architecture capable of extracting and visualizing the binding core of the peptide. Interpretation is possible through the analysis of the model graph. The proposed method is tested in the task of training a model that not only enables prediction but also facilitates determining the position of the peptide binding core and the distribution of amino acids within the core. Prediction models were trained for two types of molecules using binding data. The distributions of amino acids in the binding core match the state distributions of the model. Sequence patterns of such regions extracted using the trained models for two sets of peptide data correspond to patterns from public databases, confirming the successful validation of the method. Interpretable models provide a better description of the problem domain and help to draw a conclusion about peptide characteristics based on information extracted from the model. This information will allow researchers to better understand other steps of peptide processing involved in the immune response. For example, one can study relationships between these steps or perform a transfer of knowledge from models trained for one step to others. Using this knowledge will allow the training of the models under conditions of limited training data.

Scheduling of computing operations takes an important place in the process of distributed information processing and control systems design, especially in conditions of limited energy resources of the system. This becomes especially important for computers located on autonomous carriers, such as unmanned aerial vehicles, autonomous underwater vehicles, etc. The energy resources in such systems are limited that leads to high requirements for the energy efficiency of the carrier systems including computing ones. The paper presents the job scheduling method for a distributed computing system on a chip which allows reducing the power consumed by the system. The proposed task scheduling method includes two stages. At the first stage, jobs are assigned with the determination of an energy-efficient architecture of the system characterized by the minimum power consumption. At the second stage, jobs are scheduled taking into account the criterion that minimalizes the average job implementation time. A feature of the problem being solved in this case is the necessity of job scheduling in the system with more than one information output which does not allow applying any of the known scheduling methods to the system. The first stage of the proposed method is implemented by implementation additional processors with a simultaneous decrease in the clock frequency and supply voltage. For the second stage of the method, the job scheduling algorithm is proposed which involves the preliminary construction of a private schedule for each output of the system with further integration of these schedules into the general schedule using a heuristic procedure. The scheduling algorithm functioning is illustrated by an example of a solution for a simple system. The advantage of the proposed heuristic method is the possibility of scheduling calculations, taking into account criteria of the minimum power consumption and the minimum average residence time of a task in the system simultaniously. This makes it possible to increase the energy efficiency of solving problems in distributed computing systems on a chip, which contributes to increasing the autonomy of systems in which they are used in. The proposed algorithm has polynomial complexity, therefore, due to the relative simplicity of the algorithm, it can be used for scheduling and rescheduling jobs in real time for complex systems.

In this paper, we have developed a system for assigning customers to the routes based on their emotional state and age in Public Service Systems (PSSs). The Squeeze-and-Excitation (SE) method was used to develop the models, it improves the efficiency of the Deep Convolutional Neural Networks (DCNN) architecture by increasing the information flow between layers and enhancing important features. The method is based on compressing and exciting information at each convolution stage, which allows obtaining a vector of channel importance scores and using it to reweight the channels of the feature map. The study showed that this method allowed improving the quality of classification and reducing the model training time. The model of emotional target routing was developed based on the Newton interpolation polynomial to route customers based on their emotional state and age. The interpolation function in this model calculates the waiting time for customers according to their emotional state. Three models of binary classification of emotions and ages were developed, namely, two models for recognizing the emotional state of the customer, and one model for recognizing their age. The first and third models utilize DCNN from scratch using the new SE approach based on the attention mechanism. The second model uses the Support Vector Machine (SVM) method. The evaluate method was used to test the model after training, which allows evaluating the quality of the model on new data that was not used during training. This is done to check how accurately the model can predict the values of the target variable on new data. The evaluate method utilizes quality evaluation metrics such as accuracy, recall, and F1-score to assess the performance of the model. According to the experimental data obtained, the first and the second developed models achieved the validation accuracy of 72 % and 66 %, respectively, on the FER-2013 and Adience datasets. Their sizes were 0.69 MB and 369 MB, respectively. At the same time, the age recognition model achieved the accuracy of 88 % with the size of 1.68 MB. The mathematical model of emotional target routing (TERSS) was developed to minimize conflicts in public service systems. The developed system can automatically route customers based on their emotional state (presence of anger) and age to the appropriate operator. Thus, customers over 60 years old or with the anger level of 60–80 % are directed to a senior operator who knows how to communicate with elderly or emotionally excited customers, while customers with the anger level of 80–100 % are directed to a psychologist. This research can be applied in PSSs to detect the features of customers’ age and anger. Moreover, it can be applied in various areas where there is a contact with a large number of people, such as banks, supermarkets, airports access control systems, police stations, subways, and call centers.

Uncertain sedentary behavior has evolved as a new health concern in recent periods. Being inactive for long periods is a significant risk factor among all the adult age groups, especially over-reliance on vehicles for mobility. Sensors are making it easier to monitor seating habits throughout the active period. However, experts are divided on the most appropriate objective metrics for capturing the cumulative information of sedentary time throughout the day. Due to discrepancies in measuring methods, data processing techniques, and the absence of fundamental outcome indicators like cumulative sedentary period, evaluating the several research studies sedentary patterns was unrealistic. In this research study, a novel design was suggested with adaptive computations, namely, fleeting granularity, to differentiate instances of daily human activities. Multivariate transitory information is acquired from sophisticated units (essential cells). Our proposed scalable algorithms can identify Frequent Behavior Patterns (FBPs) with a timeframe estimate by employing collected widespread multivariate data (fleeting granularity). It has been evidenced that the applicability of the example by differentiating proof computations on two certifiable datasets. The assessment of the relationships, accuracy, and applicability of sedentary factors is the primary subject of this research.

A new method of guaranteed solution for multiclass classification problem of stochastic objects is proposed. Within the framework of the proposed approach, the classification result is a finite set of class indices which with a predetermined confidence coefficient contains the index of the class to which the object being classified corresponds. In this case, the classification itself is realized on the basis of using a classifier of the new type which is called a confidence Lipschitz classifier. The definition of the confidence Lipschitz classifier is given and its main properties have been studied. Among them, the property of guaranteed reliability of the classification which is expressed in the construction of a confidence set of limited size containing the index of the true class with a predetermined coefficient of confidence, has been studied. The case of the assembly of Lipschitz classifiers, the properties of which are formalized in the form of a theorem, is considered. We consider a practically important example of using the proposed approach in the problems of compensation of the noise process dynamics in the channels of the fiber-optic monitoring system. The proposed approach is promising for use in those classification tasks in which the number of classes has an order higher than the second, including large-scale biometric identification systems as well as multi-channel systems for monitoring extended objects.

The approach to synthesis and development of multidimensional fuzzy interval-logic regulators in the created visual programming environment that generates the program code of regulators for Simatic S7-300 and S7-400 controllers is considered. Multidimensional interval-logic regulators use the mathematical apparatus of fuzzy regulators with mixed (trapezoidal and rectangular) membership function µ equal to one. The proposed modification of regulators is the author’s development and is intended for use in control systems with a sufficiently large volume of product rules describing the logic of a complex technological object without an adequate mathematical model. The software of the visual development environment takes into account the requirements of the current editions of IEC 61131-3 and 61131-7 standards. The basic variant of the block diagram of a multidimensional interval-logic regulator is presented. Schemes for the interpretation of continuous physical quantities by an equivalent set of terms are given. The proportional deintervalization algorithm is formulated. It is shown that the synthesis and programming of this modification of fuzzy regulators consists in determining the vectors of terms of input and output continuous variables, as well as the mutual relations between them, compiling a system of production rules and selecting the appropriate algorithm of deintervalization. The approach to the development of multidimensional interval-logic regulators by means of special software tools (editors and applications) included in the visual development environment is described. The proposed approach provides a clear and quick creation of controller functional blocks for Simatic S7-300 and S7-400 programmable logic controllers. At the same time, it is possible to analyze and simulate the work of the system of production rules and regulators as a whole, which reduces the time of development and debugging of control systems based on them.

The solution of the mathematical problem of rotation of a three-dimensional surface in space with an orthogonal basis and its mapping on a plane using simple geometric shapes is considered. This task arises when accompanying moving objects against the background of the surrounding environment. A design feature of such systems is that they contain functional additional elements that provide information about the maneuvering object of observation and generate control signals to work out the error that has occurred. This operation is performed continuously in real time. It is assumed that this problem is solved using a digital computer, i.e., the change in the angle of sight of the observed moving object will be recorded in separate time intervals — partial (discrete) ones. The initial state of the coordinate system can be represented in matrix form, respectively; the transition to the final state is carried out at discrete points in time. The problem is solved analytically. A number of restrictions on the magnitude of vectors and their mutual orientation in space are formulated. The proposed approach made it possible to increase the visibility and predictability of the operations performed due to the transition from nonlinear trigonometric equations to the simplest linear operations. To demonstrate the correctness of the implementation and clarity of the application of the proposed vector-algebraic approach, the background of the environment is presented in *.off format (geomview object file format). Finite expressions are obtained for the rotation of the coordinate system of an elastic body with a fixed center of mass. The solutions obtained are formalized on the basis of strict mathematical transformations and belong to the class of problems in which analytical relations accurately describe the data, that is, when, in the absence of measurement errors, the residual vector of the system is always zero. This approach allows you to avoid performing transformations on complex nonlinear mathematical expressions.

To operate in unstructured environments, robots must have the property of passivity which can be realized either through control algorithms or physical elastic elements. Flexible elements can be used to recover energy, absorb peak shock loads, and simplify the control system, generally reducing the requirements for accurate information about the robot’s environment. The modeling of flexible bodies, for example using the finite element method, is computationally demanding, which limits the simulation of the dynamic behavior of robots with flexible elements. In this paper, we propose an approach for analytical and simulation modeling of flexible joints using the planar case of a spatial spring model, which provides high speed simulation without loss of accuracy. The synthesis of the flexible joint model consists of numerical optimization of the nonlinear stiffness diagrams of the rotational and translational degrees of freedom for the planar case of the spatial spring model. The synthesized flexible joint model allows describing the relative motion of two links. In the first step of the synthesis, the flexible joint is optimized by finite element method to find the reference data of applied load and corresponding deformations. In the second stage, an optimization problem is solved to find nonlinear stiffness diagrams for the planar case of the spatial spring model; the criterion is to minimize the error between the reference data and the optimized spring model. In the third stage, the obtained results are verified by simulation and/or physical experiment. The method of analytical and simulation modeling of flexible joints with the help of spatial spring model is proposed, the procedure of optimization of stiffness of spring model is proposed, verification in simulation environment is carried out, full-scale experiment is carried out, comparison of simulations by finite element method, simulation with the help of spring model and results of full-scale experiment is provided. The proposed method allows the calculation of a simulation model of a flexible joint approximately twice as fast as the finite element method. The proposed model of flexible joint is necessary to increase the speed of simulation modeling of mechatronic and robotic systems with compliant hinges without loss of accuracy. Approbation of the method is planned for the design of locomotion, manipulation, wearable robots, and gripper devices.

In the search for new magnetically ordered phases of materials, solid-state synthesis technologies in reaction crucibles are used. The final result of the synthesis process in reaction crucibles is conditioned, in particular, by technological factors, the mode of current flow and its density, the achieved temperature in the reaction zone, exposure time, geometrical parameters of the crucible and the reaction zone, etc. The paper presents the results of influence investigation of the reaction volume filling degree with tin melt on the processes of heat and mass transfer during its electrothermal treatment. A model describing diffusion processes in the reaction zone during the synthesis of iron and tin intermetallides under electrothermal treatment has been proposed. The diffusion process in the reaction crucibles of the iron-tin system was investigated by the finite element method in the Comsol Multiphysics software environment. It is shown that the decrease in the degree of filling of the reaction crucible with synthesis components leads to a change in the distribution of current density and a decrease in the temperature in the reaction zone, which affects the mass transfer processes. The results of the work can be used in the analysis of experimental data on the production of intermetallides by reaction synthesis and determination of the necessary technological parameters for the synthesis of new materials.

The paper proposes a modified method for measuring the refractive index of a triangular prism using an autocollimation angle measuring system designed to measure angles formed by flat surfaces of objects. The method involves using a fixed mirror to reflect the refracted beam, measurement of the angles of incidence of the beam on the face of the prism corresponding to the autocollimation positions and calculating the refractive index of the prism material using the solution of a system of equations. The paper presents the experimental study results for a triangular prism made of K8 optical glass using the proposed method, and a comparison of the results with the readings obtained using the State Primary Standard of the Refractive Index Unit GET 138-2021. The proposed method makes it possible to simplify the process of measuring the refractive index since there is no need to measure the angle of deviation of the beam.