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Bitter I. Local limit theorem for a perturbed sample paths of induced order statistics

In this paper we derive a local limit theorem for a perturbed sample paths of normalized sums of induced order statistics obtained from a sequence of independent identically distributed random vectors under weak regularity conditions on the coefficients. The situation under consideration is a typical example of the problem of estimating the rate of convergence of discrete-time Markov processes to diffusions, when the corresponding trends and diffusion coefficients of the Markov chain and the diffusion limit coincide only asymptotically. Under the conditions described above, the classical result of Konakov and Mammen (2000) on the rate of weak convergence of triangular arrays of discrete Markov processes to a diffusion process with coefficients that coincide with the coefficients of the chains turns out to be inapplicable. Our approach is based on the study of the uniform distance between the transition densities of the underlying inhomogeneous Markov chain and the limiting gaussian diffusion process. In particular, the convergence rate estimate derived from the well-known classical limit theorem and the parametrix-type stability bounds.

Sysoev A., Pogodaev A., Saraev P. Reduction of hierarchical models: researching sensitivity by factors using analysis of finite fluctuations

The selected class of mathematical models determines the methods used in the study of a system or process and approaches to their control. One of the directions of model structure control is its reduction, understood as a reduction in the number of factors in order to build a less computationally expensive model. This problem can be referred to the concept of mathematical remodeling --- building a new model on the basis of a known one. Among the ways of solving such a problem is the Sensitivity Analysis of the model by factors, which can be carried out in various ways. One of these ways is based on applying the method of Analysis of Finite Fluctuations to estimate sensitivity measures. This method is based on the use of Lagrange mean value theorem. The mentioned theorem delivers an exact decomposition of the finite increment of a model's response as a weighted sum of the finite increments of its factors. The paper describes an approach that allows performing Sensitivity Analysis of this type at each of the levels of a hierarchical system, as well as an end-to-end analysis that involves finding estimates of the influence measures of the model outputs of the preceding levels on the output of the model of the upper level. Numerical examples demonstrating the applicability of the method are presented. Classical full-connected neural networks are used as a class of models describing the hierarchical levels of the system.

Scherbov I. Аlgorithm operation for adaptive nonlinear smoothing of multiparameter measuring data

The paper considers the operation of an adaptive nonlinear smoothing algorithm for multiparameter measurement data. This algorithm allows for the joint processing of measurement data with spatial and temporal redundancy, which improves the accuracy and reliability of determining the secondary parameters of the test objects' positions. The algorithm uses structures of linearly independent and ?-orthogonal basis functions, which allow for the joint processing of various types of measured primary coordinates of the test objects' positions obtained from external trajectory measuring instruments, to obtain independent estimates of the smoothing polynomial coefficient vector. The proposed method for selecting the initial approximation of the smoothing polynomial coefficient vector to begin the iterative process of finding the most reliable value of the smoothing polynomial coefficient vector at the first smoothing step allows for each subsequent step of locally moving smoothing of the measurement data to use the value obtained at the previous step of locally moving smoothing. The applied in the work algorithm methods of checking the significance of the coefficients of the smoothing polynomial, allowed to optimize the process of determining the significant coefficients of the smoothing polynomial. The application of the developed method of selecting the initial approximation of the vector of coefficients of the smoothing polynomial and the proposed methods allowed to reduce the time for processing the data of trajectory measurements. According to the results of the conducted experimental study it was established that the developed algorithm of adaptive nonlinear smoothing of data of multiparameter trajectory measurements increases the accuracy and reliability of determining the secondary coordinates of the spatial position of the aircraft in trajectory measuring and computing complexes and ensures stability in operation when processing measurement data with failures and gross measurement errors.

Romadov S., Kozyr A., Efromeev A. Study of the characteristics of linear flexible object control system

The paper solves a flexible object control problem. The issues of constructing a mathematical model of an inhomogeneous flexible link based on the Euler-Bernoulli equation are considered. The simple design model was chosen, which, for example, can describe the vibrations of a single-link manipulator, load bending during aerial transportation, or a helicopter blade. A universal algorithm for determining the parameters of an elastic system is presented. A convenient method is used to analytically determine mode shapes of an inhomogeneous structure. Vibrations model was built by the method of initial parameters with discretization of distributions of mass and bending rigidity. The system dynamics equations are obtained by integrating the Euler-Bernoulli equation, which makes mathematical formulation universal. The resulting mathematical model describes with sufficiently high accuracy the dynamics of objects, which are characterized by a constant or stepwise distribution of mass and stiffness along their length. The control system, providing high speed with minimal fluctuations, is developed using LQR and LMI methods. It is shown that the LMI method allows one to directly limit the control action and more intuitively set the required characteristics of the system, however, it is less resistant to changes in the parameters of the control object. Control system needs to be done more robust, and thus further research is necessary.

Antipov A., Greznev P. Two approaches to synthesizing the end-point control law of a two-link manipulator

For a two-link manipulator endpoint, we consider the problem of tracking the desired trajectory defined on a plane in the endpoint workspace under the action of external disturbances. These perturbations are assumed to be matched (acting along the same channels with the controls, which are considered to be generalized torques). Standard approaches to control rely on the solution of the inverse problem of kinematics, which can be ambiguous and, as a rule, requires the use of numerical methods. Given these drawbacks, the problem of developing control laws without solving the inverse kinematics problem is relevant. To create such an approach to control, we consider the coordinates of the endpoint in the Cartesian system as output variables. Then, on the basis of the unambiguous dependence of the output on the generalized coordinates, we can transform the initial description of the system in terms of generalized coordinates to a description in terms of the endpoint positions and solve the problem of control synthesis on the basis of the transformed system. The control is constructed using the block approach, which allows us to divide the problem into two subproblems of synthesizing virtual and true controls in fully actuated subsystems. For comparative analysis, we also developed a method for synthesizing control torques, which involves solving the inverse problem of kinematics. In both methods, smooth and bounded S-shaped feedback is used, which suppresses disturbance with a given accuracy and monotonicity of transients. Numerical simulation results are presented to confirm the effectiveness of the proposed approach without solving the inverse kinematics problem.

Glushchenko A., Lastochkin K. Placement of input and output in given sets for one class of systems

In [3, 15], a control method providing the nonlinear plant inputs and outputs in given sets is proposed. The main theorems of these studies are valid for SISO and MIMO systems with arbitrary relative degree. However, constructive algorithms for control law design are proposed for systems with unit relative degree only. In this study, the above-mentioned results are extended to a class of SISO systems with arbitrary relative degree and stable internal dynamics. For such a class of systems, a new control law providing the plant inputs and outputs in given sets is proposed that ensures compensation of both parametric uncertainty and exogeneous perturbation. In such a solution, the control signal boundedness is guaranteed explicitly by using a smooth nonlinearity in the control law, which prelimitly approximates the saturation function, and when the control signal amplitude is not enough to keep the system output in a given set, the proposed solution dynamically changes the given set for the system output, which allows one to avoid the feedback signal discontinuities. The theoretical results are validated via numerical experiments and can be applied, for example, to control position and Euler angles of solid bodies.

Rubinovich E., Yurchenkov I., Nazarkin V. Method of signal extrapolation on two-dimensional antenna system using deep neural network algorithms to solve the super-resolution problem

The article deals with methods of remote sensing of objects using digital antenna arrays (DAA). This approach allows obtaining information about objects without direct physical contact by analyzing the radiation reflected or emitted by them. The features of the formation of the directional pattern (DN) of a DAA consisting of a two-dimensional flat rectangular array of radiating elements are described. The mathematical model of the DN of an individual radiator and the system as a whole is presented taking into account the wave number, the distance between the elements and scanning angles. Special attention is paid to the limitations of the resolving power of the system due to the Rayleigh criterion and related to the linear dimensions of the antenna. In the region of small angular deviations the model components are approximated, which simplifies the calculation, but limits the possibility of distinguishing closely located sources. The problem arises of digital processing of the received signals to increase the angular resolution of the system. The article discusses methods and algorithms based on deep neural networks, aimed at overcoming these limitations and improving the quality of acquired images in remote sensing using DAA. The article demonstrates qualitative results of the proposed solution on the DAA with fixed parameters. Examples of the work of the considered algorithm are shown visually.

Farkhadov M., Teplukhin R., Abramenkov A. et al. Lucas – Kanade optical flow computation based on the finite dimensional sampling theories

This paper considers Lucas – Kanade optical flow computation using the finite dimensional sampling theories based on Fourier transform. Such a procedure regards all image pixels for image derivative evaluation and is able to provide high accuracy of optical flow computation. This paper proposes a hybrid image differentiation method which combines the finite dimensional sampling theories with Scharr operator in order to improve accuracy of optical flow computation. Experiments on optical flow computation for real videos on the basis of the finite dimensional sampling theories as well as the hybrid method have been conducted and their results are presented. Leveraging of the finite dimensional sampling theories allows to improve accuracy of optical flow computation for videos including poor illumination and shaded regions. The research results can be applied in various computer vision tasks such as visual object tracking.

Shiroky A. Impact of internal configuration on overall risk in complex systems, examined through the risk reduction problem in a system of star-shaped structure

This paper explores how the internal structure of a complex system affects its overall risk. Addressing risk management challenges often requires considering structural effects such as risk transfer and failure propagation. The study examines how the positioning of elements within a predefined star-shaped structure affects the overall risk of the system. The author shows that analytically solving the issue of optimal element placement to minimize risk in this configuration is not feasible and introduces an algorithm with bounded errors to tackle this problem. When considering equal expected damages from a potential attack on any element, the author provides upper bounds for the relative error of the proposed algorithm and suggests a method for quick risk assessment in systems with a ``star'' configuration. Additionally, he has derived an exact solution for the optimal placement problem when the risks of the elements share a specific ratio. The obtained results will be used in further research for the resolution of an ambiguous problem in more intricate structures, particularly tree-like structures, with subsequent generalization to complex networks of arbitrary topology.

Bulavchuk A., Semenova D. On the project scheduling problem with the criterion for optimizing the economic effect from the use of emission quotas

The paper considers a new project scheduling problem with the criterion of maximizing the economic effect of using emission quotas. The authors formulated a problem model that takes into account the peculiarities of the emerging practice of handling carbon units in Russia. The model provides for the possibility of selling unspent carbon units. The impact on the economic effect of fines for overspending quotas is also taken into account. The statement with deterministic characteristics and two non-deterministic varieties -- stochastic and fuzzy -- are analyzed. When describing projects, it was believed that emission values could be non-deterministic. In the stochastic statement, the case is analyzed when the model parameters are independent and have a Weibull -- Gnedenko distribution. For this case, a variant of comparing schedules using first-order stochastic dominance is proposed. In the fuzzy statement, fuzzy triangular numbers were used to describe the project. A ranking function was used to select the best schedule. For each statement, approaches to solving the problem based on modifications of the GASPIA and SASPIA algorithms are demonstrated. The modified GASPIA algorithm used a new crossing scheme. For a conditional example of the project, computational experiments were conducted demonstrating the applicability of the proposed algorithms to solving the problem.

Maryasin O., Tihomirov L. Detecting point anomalies in energy consumption data using unsupervised machine learning methods

The paper describes studies on detecting point anomalies in energy consumption data using two different data sets as an example. Methods for constructing typical energy consumption patterns are considered and the authors' method for constructing a typical daily energy consumption profile is presented. To conduct numerical experiments, the authors selected 21 unsupervised machine learning methods suitable for detecting point anomalies. Based on the results of numerical experiments, the methods that most successfully coped with the task of detecting point anomalies were noted. Particular attention in the work was paid to methods that do not require additional parameters and modern, promising methods based on artificial neural networks. According to the test results, the best algorithms were statistical algorithms based on constructing histograms. One of the main problems addressed in the work is the problem of setting the contamination parameter for each considered algorithm. One of the solutions to this problem is the use of threshold algorithms. It is shown that if the original algorithm does not detect anomalies well enough (the contamination parameter is not configured), then the use of threshold algorithms can significantly improve the accuracy of anomaly detection. Threshold algorithms are noted, the use of which for the tasks of analyzing anomalies in energy consumption data, most often ensures an increase in accuracy. Threshold algorithms can be applied both to the results of individual anomaly detection algorithms and to the results of ensembles of algorithms obtained using various combination strategies.

Makhankova I., Druzhinin P. Modelling excess mortality during the pandemic period among federal districts of the Russian Federation

The pandemic has affected all spheres of life in all regions of the Russian Federation and has had an impact on the temporary increase in mortality in Russia. The calculations show that the pandemic occurred in two waves, each consisting of three parts, with peaks of high excess mortality. The purpose of this article is to use mathematical models to calculate excess mortality by federal districts, taking into account data from the latest all-Russian population census, and to analyze the impact of COVID-19 on excess mortality in Russia. When calculating excess mortality, the first method took into account mortality in the previous period (2019), the second method is based on calculating the downward trend in mortality in 2019 compared to 2018, the third combined statistical method SARIMAX takes into account mortality trends since 2015. The result of the modeling is a quantitative assessment of excess mortality in Russia during the pandemic period. The pandemic can explain 57% of excess deaths in 2020-2021. A mortality forecast for 2023 has been compiled in the context of federal districts. The results can be taken into account when developing forecasts for the socio-economic development of Russia for the long term in terms of health protection of the population.

Grushevsky A., Ilyinskaya E., Finogeev A. Methodology and tools for optimizing the duration of the traffic light cycle

One of the main elements of traffic and pedestrian flow control in the road environment is traffic light regulation. Automation of traffic light regulation allows calculating the optimal modes of its operation in order to reduce delays in traffic and waiting time for vehicles to pass through intersections, and reduce the likelihood of traffic jams. The result is increased road safety and sustainability of the urban transport system. The article considers the development of a model, methodology, and tool for calculating the optimal traffic light cycle steps. The relevance of the article is due to the fact that the growth of road traffic reduces the efficiency of vehicle use, increases the time of delays and stops, fuel consumption, and increases the number of traffic accidents and violations. The object of the study is an adaptive traffic light control system at intersections. The purpose of the study is to analyze and develop a mathematical model and methodology for calculating traffic light cycle steps depending on current traffic conditions at intersections in order to reduce the waiting time of vehicles and pedestrians. The result of the research is a developed software application that implements the proposed method for calculating the optimal duration of the traffic light cycle depending on the intensity of automobile and pedestrian traffic and the length of the queue.

Korgin N., Meshcheryakov R. The concept of a distributed network of test grounds for scenarios' assessment for the use of heterogeneous groups of electric vehicles in complicated climate and terrain environment - implementation examples and development prospects

The article describes a project of the distributed network of test grounds for scenarios' assessment for the use of heterogeneous groups of electric vehicles in complicated climate and terrain environment for field research support in the interests of scientific organizations and operating the instrumentation base of unique scientific installations and the prospects for its further development. The article describes a general approach based on the concept of active planning from the theory of organizational systems, the results of experimental testing of individual elements of the concept on three pilot network nodes based on the infrastructure of regional centers of the RAS located in regions with complex climatic and landscape conditions, and directions for further development of the project. A formal mathematical model is proposed that allows describing the process of coordinating interests within a single network node as a center for collective use with expandable functionality and number of users. In conclusion, a further program of scientific research is proposed on the problem of the functioning of a heterogeneous group of electric-powered vehicles as elements of a small distributed energy system based on the developing network of testing grounds.

Podvesovskii A., Filonov A., Venets V. et al. Decision making model for reconfiguration of heterogeneous group of interacting cyberphysical system objects

The control of the interaction of cyberphysical system objects within a heterogeneous group necessitates the completion of a series of tasks, among which we can identify the tasks of group configuration control, including the formation of the initial configuration, the optimization of the spatial location of objects, the distribution of targets, and the reconfiguration of the group. The importance of the task of group reconfiguration is due to the importance of ensuring and preserving the integrity of the group in conditions of reduced capabilities, for example, due to the failure of individual members of the group. This paper considers the reconfiguration of a two-level group of heterogeneous interacting objects of a cyber-physical system. It does so on the basis of the reconfiguration of a two-level group of unmanned aerial vehicles, which have been constructed according to the scheme "master-subordinate." In order to address this issue, we propose an approach for developing a decision-making model that reduces the problem to a set of pair-combinations in accordance with the "many to one" scheme. A procedure for the formalization of preferences is presented, along with an algorithm for the formation of an optimal configuration. This algorithm is a modified Gale-Shapley algorithm for a two-sided matching model with a dynamic real quota. The results of the experimental study of the algorithm, and ways to eliminate the shortcomings identified are presented and discussed. The conclusion presents a comprehensive overview of possible directions for further advancement of the proposed approach to constructing a decision-making model for the reconfiguration problem.

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