
Main / Mathematical modeling
Section: "MATHEMATICAL MODELING"
Aleksandr Sergeevich Andreev, Ulyanovsk State University, Doctor of Sciences in Physics and Mathematics, Professor; graduated from the Faculty of Mechanics and Mathematics of Tashkent State University; Head of the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles, textbooks, and a monograph in the field of stability theory and the motion control of mechanical systems. [email: AndreevAS@ulsu.ru]A. Andreev,
Olga Alekseevna Peregudova, Ulyanovsk State University, Doctor of Sciences in Physics and Mathematics, Associate professor; graduated from the Faculty of Mechanics and Mathematics of Ulyanovsk State University; Professor of the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles, textbooks, a monograph in the field of the theory of stability and motion control of mechanical systems. [email: peregudovaoa@gmail.com]O. Peregudova


Robust Motion Stabilization of a Mobile Robot with OmnyWheels
The modelling as well as the design and widespread use of wheeled mobile robots in the industrial and social spheres is one of the areas of rapid development of robotics. A sufficiently large class of such robots consists of wheeled robots with rollerbearing or omniwheels. A distinctive feature of the design of such wheels consisting in the fact that the rollers are fixed to them according to a certain scheme allows the robot to move in any direction without a prior turn. This achieves high maneuverability compared to other wheeled carriages. The paper investigates the trajectory tracking control problem of a mobile robot with three omniwheels and with an offset center of mass, i.e. when it is assumed that the center of mass of the robot does not coincide with the geometric center of the platform. Previously, such a problem was not considered. The paper substantiates the control structure that provides tracking of a given trajectory, including taking into account the delay and discreteness of the signal in the feedback. At the same time the control has the property of robustness which consists in the fact that its parameters do not depend directly on the massinertial parameters of the system and the tracked trajectory. The controller is constructed only by using the values of the system parameters bounds. The result has been achieved on the basis of the development of direct Lyapunov method in the study of the stability of nonautonomous systems obtained in the previous papers of the authors. The results of numerical modeling of the problem studied are presented. Wheeled mobile robot, robust control, stabilization, trajectory tracking, Lyapunov functional.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Ivan Iurevich Davydov, Ulyanovsk State Technical University, graduated with a Master degree from Ulyanovsk State Technical University in Telecommunication Technologies and Communication Systems; a postgraduate student of the Department of Telecommunications of Ulyanovsk State Technical University; an author of articles in the field of errorproof coding and information security. [email: 1Davydov2i@gmail.com]I. Davydov,
Denis Aleksandrovich Kozlov, Ulyanovsk Transport (Aviation) Security Center, graduated from the Ulyanovsk Institute of Civil Aviation; Head of Ulyanovsk Transport (Aviation) Security Center; a postgraduate student of the Department of Aviation Security Assurance at the Ulyanovsk Institute of Civil Aviation named after Chief Air Marshal B.P. Bugaev; an author of articles in the field of aviation security. [email: peccab@mail.ru]D. Kozlov,
Sergei Valentinovich Shakhtanov, Nizhny Novgorod State University of Engineering and Economics, Cgraduated from the Leningrad Higher Military Engineering School of Communications; Senior Lecturer of the Department of Infocommunication Technologies and Communication Systems at the Nizhny Novgorod State University of Engineering and Economics; an author of publications in the field of errorproof coding and information protection. [email: r155p@bk.ru]S. Shakhtanov,
Mariia Iurevna Shibaeva, Nizhny Novgorod State University of Engineering and Economics, graduated from the Faculty of Information Technologies and Communication Systems at the Nizhny Novgorod State University of Engineering and Economics; Master’s Degree Student of the Department of Infocommunication Technologies and Communication Systems at the Nizhny Novgorod State University of Engineering and Economics; an author of publications in the field of errorproof coding and information protection. [email: shibaevamarya@yandex.ru]M. Shibaeva


Permutation Decoding in the System of Combinations Code Designs in the Evaluation of Biometric Data
Stateoftheart telecommunication systems and means of data protection against natural and anthropogenic interference in the form of redundant codes are increasingly used in various applications related to the processing of biometric data. A large volume of publications in this subject area is devoted to codes with a low density of parity checks, polar codes, turbocodes with iterative data transformations that implement the algorithm of "belief propagation". These code constructions provide the required probabilistic characteristics but the procedure of decoding such codes takes long time intervals, which is unacceptable in terms of the duration of the cycle of biometric data management in systems critical to time delays. The paper proposes to use the principle of permutation decoding (PD), which is applied to systematic block codes. This method allows to fully use the corrective capabilities of redundant codes but in the classical interpretation requires cumbersome matrix calculations, which does not allow to use the positive properties of the method for error correction. The complexity of the computational process is excessively high. Therefore, to reduce the negative effect in the PD system, it is proposed to use the cognitive principle of data processing at the channel level, which significantly reduces the complexity of the decoder implementation and ensures the use of PD in the control systems of biometric data of subjects, for example, in the automation of transport security processes. Special attention is paid to the combination of codes in the format of cascade coding. For the first time, a description of such a scheme is given for polar codes and nonbinary ReedSolomon (RS) codes. Soft symbol solution, permutation decoding, cognitive map decoder, concatenated code.



Sections: Mathematical modeling
Subjects: Mathematical modeling, Artificial intelligence. 
Marina Viltalevna Samoilenko, Moscow Aeronautical Institute of National Research University, Candidate of Science in Engineering, Associate Professor; graduated from Moscow Aeronautical Institute and Moscow Institute of Physics and Technologies; Associate Professor at Moscow Aeronautical Institute of National Research University; an author of monographs, articles, and inventions; scientific interests are in the field of signal and image processing. [email: Samoi.Mar@mail.ru]M. Samoilenko


MatrixIterative Method of the Blurred Images Restoration
A new method of the pictureoriginal restoration from the blurred image is proposed. This method is based on the matrixiterative method developed by the author for solving the simultaneous linear algebraic equations. When implementing the imagerestoration method, the author uses a prior information specified. It is assumed that the intensity of minimum background values of this image as well as the point spread function are known. The task of image restoration is resulted in the solution of an underdetermined system of linear algebraic equations. A pseudoinverse technique of its matrix is a known solution of the simultaneous linear algebraic equations. The wellknown image restoration method based on this solution is also given. The author compares the image restoration by the use of this wellknown method and a new matrixiterative method based on computer simulating. It is shown that the matrixiterative method provides almost exact restoration under certain conditions. Such condition is a low occupation level of an image being filled up with objects if there is a high occupation level of an image being filled up with background values. The additive noise impact and an expected uncertainty were not considered. Simultaneous linear algebraic equations, matrixiterative method, image restoration, point spread function, pseudoinverse technique.



Sections: Mathematical modeling
Subjects: Mathematical modeling, Artificial intelligence. 
Valerii Vladimirovich Kozhevnikov, Scientific Research Technological Institute of Ulyanovsk State University, Candidate of Science in Engineering; graduated from the Pushkin Higher Command School of Radioelectronics; Senior Researcher at the Scientific Research Technological Institute of Ulyanovsk State University; an author of articles in the field of microelectronic system design theory.[email: vvk28061955@mail.ru]V. Kozhevnikov


The Method of Mathematical Modeling of Cognitive Digital Automata
An approach to solving the problem of mathematical modeling of cognitive digital automata (CDA) is proposed. The task of formalizing the concept of the cognitive nature of the CDA mathematical model comes to the fore. The cognitiveness (cognition) of the mathematical model is determined by the possibility of learning and generating solutions that are not provided for in the learning process. A special feature of CDA is that the description of the neural network (NN) structure is used as a structural circuit of the automata, and the logical function "NOTANDOR" is used as the model of the neuron. In the case of the feedbacks formation from the output to the inputs of the neurons, the model of the neuron is a binary trigger with a logical function "NOTANDOR" at the input. As a tool for constructing a mathematical model of CDA, a mathematical apparatus of Petri nets (PNs) is proposed: marked graphs, inhibitory PNs and PNs with programmable logic. The mathematical model is builton the basis of the representation of the CDA in the form of the state equation of the PNs from the class of Murat equations (matrix equations) or a system of linear algebraic equations. The task of formalizing the concept of cognitiveness (cognition) is solved as a result of the logic synthesis (learning) of the initial structural circuit of CDA or the formation of the formula (network algorithm) of CDA. At the same time, the possibility of forming a formula (network algorithm) of CDA depends on the critical mass (quality) of training sets and training algorithms. Hence, the task of generating the minimum set of training sets for a given CDA function or experimentally determined function takes on particular importance. Forecasting or generation of solutions, in turn, is performed on the basis of the mathematical model of CDA obtained in the learning process. intellectual control system, cognitive digital automata, artificial intelligence, neural networks, machine learning, cognition, Petri nets, equation of states, mathematical modeling, synthesis, generation, analysis, logic.



Sections: Mathematical modeling
Subjects: Mathematical modeling, Artificial intelligence. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Doctor of Science in Engineering; graduated from the Faculty of Physics at Irkutsk State University, completed his postgraduate study at Bauman Moscow Technical School, doctoral study at Ulyanovsk State Technical University; Chief Staff Scientist of FRPC JSC 'RPA 'Mars'; an author of monographs, text book, articles in the field of the mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]I. Egorov,
Vladimir Aleksandrovich Baboshin, St. Petersburg National Guard Forces Command Military Institute, Candidate of Sciences in Engineering, Associate Professor; graduated from Ulyanovsk Higher Military Command College of Communications; Associate Professor at the Department of Informatics and Mathematics of St. Petersburg National Guard Forces Command Military Institute; an author of articles and inventions in the field of the analysis and synthesis of information systems and mathematical modeling. [email: boboberst@mail.ru.]A. Moiseev,


Models for Creating the SpecialPurpose Mathematical Support of ComputerAided Control Systems
Authors provide reasons to a promising outlook for creating a technology for the development of specialpurpose mathematical support of the computeraided control system in order to improve the management based on process automation of contentrelated information processing and decisionmaking support. Different specialpurpose software components as well as their development stages are analyzed. A block diagram of specialpurpose mathematical support creating that includes production volume data at each stage and intensity of its growth and decrease. Linear differential equations build the mathematical models for creating the specialpurpose mathematical support. Analytical decisions have been made, curves demonstrating the production volume change at all stages are provided. For mathematical modelling the processes of specialpurpose mathematical support creating and decisionmaking support, authors use the LotkaVolterra equations that demonstrate the creative behavior of designers’ work. The equations obtained are examined for stability. Authors detect approximate decisions. The models built are designed for optimal source distribution among development stages of all the specialpurpose software types. Specialpurpose mathematical support, design technology, mathematical modelling.



Sections: Automated control systems
Subjects: Automated control systems, Mathematical modeling. 
Dmitrii Andreevich Grigorev, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Master’s Student; graduated from the Faculty of Informatics and Computer Engineering of Ulyanovsk Polytechnic Institute; Leading Software Engineer at Federal ResearchandProduction Center Joint Stock Company ‘RPA ‘Mars’; an author of articles in the field of airdefense processes automation. [email: mars@mv.ru]D. Grigorev,
Tatiana Nikolaevna Maslennikova, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Candidate of Science in Engineering; graduated from the Radioengineering Faculty of Ulyanovsk Polytechnic Institute; Head of a research laboratory in FRPC JSC ‘RPA ‘Mars’; an author of articles in the field of information support of computeraided systems of specialpurpose. [email: mars@mv.ru]T. Maslennikova,
Aleksandr Nikolaevich Piftankin, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Candidate of Science in Engineering; graduated from the Faculty of Mechanics and Mathematics of Ulyanovsk State University; Chief Specialist at FRPC JSC ‘RPA ‘Mars’; an author of articles inthe field of automation of complex radar information processing, planning of fighter aircraft actions and control processes. [email: mars@mv.ru]A. Piftankin,
Anastasiia Vladimirovna Polovinkina, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Candidate of Sciencs in Physics and Mathematics; graduated from the Faculty of Mathematics and Information Technologies of Ulyanovsk State University; Software Engineer at FRPC JSC ‘RPA ‘Mars’; an author of articles in the field of basic algebra and complex processing process automation. [email: mars@mv.ru]A. Polovinkina


The Mathematical Model of Air Defense Control Process
The article deals with problems on shipborne antiaircraft defense (AAD) system control process. The development of a plan for distribution of shipborne air defense systems through enemy objects is a one of the main stages of this process. The distribution plan represents an assignment array, the element of which includes identifiers for the air object and AAD facilities and is assigned for that air object. The distribution plan is generated with ranking of air objects on a danger level, evaluating the capabilities or efficiency of the AAD facilities assignment to air objects, and generating the plan of AAD facilities distribution through air objects according to the given efficiency criterion. When solving this problem, it arises the necessity of considering not only the actual state of the system but the predicted one. Authors suggest a mathematical model that considers jointly planning processes (problem solving on the predicted state) and control processes (problem solving on the actual state) of AAD facilities. The model takes into account the using of multiplex means and their loading features as well as the dynamics of evolving events. Antiaircraft defense (AAD), mathematical models, antiaircraft weapon, distribution plan, assignment criterion.



Sections: Automated control systems
Subjects: Automated control systems, Mathematical modeling. 
Aleksei Arkadevich Smagin, Ulyanovsk State University, Doctor of Science in Engineering, Professor; graduated from the Faculty of Radioengineering of Ulyanovsk Polytechnic Institute; Head of the Department of Telecommunication Technologies and Networks of Ulyanovsk State University; an author of articles, inventions, and monographs in the field of information system development of different purposes. [email: smaginaa1@mail.ru]A. Smagin,
Iulia Aleksandrovna Radionova, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Candidate of Science in Engineering; graduated from the Faculty of Mathematics and Mechanics of Ulyanovsk State University; finished her postgraduate study at Ulyanovsk State Technical University; Lead Programming Engineer at FRPC JSC ‘RPA ‘Mars’; an author of articles in the field of automated workflow systems, intelligent technical documentation storages, and statistical analysis of supplier appraisal. [email: juliaowl@mail.ru]I. Radionova,
Sergei Aleksandrovich Karpaev, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Postgraduate Student; graduated from Ulyanovsk State Technical University; Production Control System Engineer at FRPC JSC ‘RPA ‘Mars’; an author of articles in the field of the business software automation and shortterm production planning. [email: neonix3000@mail.ru]S. Karpaev


Operatingresource Model of Technological Operations Distribution Based on the Implementation Means
The article is devoted to the actual topic of designing route maps. At the heart of the route maps, the route for performing technological operations at the production site is laid. In the production process, production is often stopped due to imperfections in the route map, one of the reasons for which is the change of resources.In the article it is proposed to carry out the design of the technological route according to the proposed principles with the use of a twopass twocomponent model as an increase in the productivity of the production process. The methodology is based on the principle of selecting the means for implementing technological operations on the basis of two interacting models, which make it possible to cover the process more fully from the point of view of resource provision and the performance of a technological operation using the example of chemical production.The proposed model allows the designer to choose the route of the technological process from the set of proposed options. An algorithm for designing and implementing a model in automated systems is presented.The offered algorithms allow to form design decisions, it gives the chance of their use for the subsequent processing and definition of efficiency.Formed by different criteria, technological routes provide many variants of the solutions obtained. The offered provides efficiency of improvement of quality of technological processes due to use of means of information support of maintenance of a set of operations close to an optimum choice of technical means of realization. Algorithm for designing design solutions, tool support, mathematical model, design methodology, operational resource model, design of route maps of technological processes, technological processes, chemical production.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Marina Vitalevna Samoilenko, Moscow Aeronautical Institute, Candidate of Science in Engineering; graduated from Moscow Aeronautical Institute and Moscow Institute of physics and Technologies; Associate Professor at Moscow Aeronautical Institute (of National Research University); an author of articles, monographs and inventions; scientific interests are in the field of signal and image processing. [email: Samoi.Mar@mail.ru]M. Samoilenko


Reconstruction of the Point Spatial Coordinates in the Case of Normal Stereo Photography
The article presents a solution for the problem of a point spatial coordinates reconstructing in a base coordinate system by its two stereo images. Author solves the problem for the case of identical cameras application which optical axes are mutually parallel and orthogonal to the stereoscopic basis. This taking photo is called in photogrammetry as a normal photographing. Author provides a computational simplicity of a point spatial position recovery algorithm. But in classical photogrammetry this computational simplicity is provided only under additional restrictions: cameras should locate at the same height, images should be horizontal and the base of stereoscopy  parallel to the horizontal axis of the base coordinate system. For another camera positions, it will be necessary to use additional spatial similarity transforms which complicate computations.Solution presented in the article differs from the photogrammetric method by its universality: neither additional conditionsare imposed to the positions of the cameras and images. And at the same time, it has computational simplicity comparable with the photogrammetric method of normal photography with additional restrictions. Methodologically, decision presented in the article is based completely on the application of vectormatrix approach from the problem formulation up to the final result. Structurally, it differs from the photogrammetric method by its symmetry with respect to of the cameras and images parameters: cameras are equivalent when determining a point spatial coordinates, while the photogrammetric solution is based on the coordinates on one image, the other one is used for the scaling factor determination.The universality of the presented solution and its computational simplicity are proved by the results of computer experiments. Stereo images, point spatial coordinates, central projecting, vectormatrix equation, photogrammetry, normal photographing.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Dmitrii Vladimirovich Ganin, Nizhny Novgorod State University of Engineering and Economics, Candidate of Science in Economics; graduated from the Nizhny Novgorod Academy of Agricultural Sciences; ViceRector for Research and Innovation Affairs, Associate Professor at the Department of Information and Communication Technologies and Communication Systems of the Nizhny Novgorod State University of Engineering and Economics; an author of articles and patents of the Russian Federation in the field of errorcorrecting coding and data recovery systems. [email: ngiei135@mail.ru]D. Ganin


Permutation Decoding in the System of Coherent Networks
The principle of matching highspeed optical communication systems at the data link layer using permutation decoding of redundant codes is considered. The expediency of such an approach is proved when applying the cognitive data processing procedure. Author indicates the parameters of such systems. Considering the widespread use in data exchange systems and in automatic control systems, in computing systems and similar computing devices of nonbinary noiseresistant Reed Solomon (RS) codes, a subtle analysis of the complexity of decoding such codes using the permutation method is carried out. The estimation is made according to the number of code vectors of elementary arithmetic operations performed in the decoding procedure. Two approaches are compared: firstly, the classical principle of decoding RS codes, secondly, the permutation decoding method using a cognitive map. It is shown that the results obtained for rearrange decoding can be generalized for other code structures, including those implemented on the basis of binary codes. Various approaches to the formation of soft solutions for nonbinary symbols of RS codes are presented and a likelihood ratio method is proposed which is based on comparing the obtained sequence of estimates of a nonbinary code symbol with some predetermined reference set of estimates. The expediency of using the analyzed method in a number of important applied areas is proved. Coherent network, nonbinary redundant code, cognitive map, fast matrix transformations.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Vladimir Kuzmich Manzhosov, Ulyanovsk State Technical University, Doctor of Science in Engineering; graduated from the Engineering Faculty of Frunze Polytechnic Institute; Professor at the Department of Industrial and Civil Engineering of Ulyanovsk State Technical University; an author of articles, monographs, inventions in the field of dynamics of machines, impact processes modeling. [email: v.manjosov@ulstu.ru]V. Manzhosov,
Aleksandr Anatolevich Samsonov, Ulyanovsk State Technical University, graduated from the Dimitrovgrad Institute of Technology, Management and Design of ULSTU; Postgraduate Student of Ulyanovsk State Technical University; an author of articles and patents in the field of creation of mechanisms of various technological purposes. [email: tpm@ulstu.ru]A. Samsonov


The Functioning of the Lever Mechanism for Automated Capture of Solid
The article is devoted to the problem of functioning of the lever mechanism in the automated capture of a solid body. In technological systems such mechanisms are used to lift and move solid cylindrical bodies. The task of the mechanism is an ability to hold a solid body due to friction forces in the capture zone. Friction forces in the contact zone of the driven link with the surface of the body exclude the possibility of breaking the connection between the solid and the driven link. The gripping force depends on the magnitude of the driving force and the parameters of the lever mechanism gripper. The model of the lever mechanism of capture is constructed. The ratio of the force at the leading link and the arising normal reaction in the contact zone of the driven link with the cylindrical surface is established. The influence of the mechanism parameters on the ratio of these forces is determined. The zones at which the force ratio reaches the lowest values are shown. Model of lever mechanism, automated capture, friction forces, angle of motion transmission.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars, Doctor of Science in Engineering; graduated from the Faculty of Physics of Irkutsk State University, completed his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’; an author of monographs, a manual and articles in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


Construction and Application of an Analytical Approximation of Threedimensional Distribution
The algorithm and software for solving a threedimensional distribution problem in the forming of control loops are developed. Experimental research has been carried out. The dependence of the solution time on the dimension of problem determined by the number of control objects, observation means and environmental objects that form control loops has been obtained. A mathematical model of the control loop formation is constructed with the choice of optimal values of the adjustable parameters of control objects and observation means. A solution algorithm is described generally with the optimal distribution being performed at each step of searching the optimal values of adjustable parameters. A solution algorithm is proposed on the basis of an analytical approximation of the threedimensional distribution, which ensures the practical implementation of highdimensional problems with restrictions on time. An approximation equation for the three dimensional distribution is obtained using an analytical approximation of the twodimensional distribution. The equation was verified with experiments proved that it is possible to use it in highdimensional problems. A mathematical formulation and an algorithm for solving the problem of control loop formation are given based on the mobility of control objects and observation means. Control loop, threedimensional distribution, mathematical model, algorithm for solving, analytical dependence.



Sections: Automated control systems
Subjects: Automated control systems, Mathematical modeling. 
Innokentiy Vasilyevich Semushin, Ulyanovsk State University, Doctor of Science in Engineering, Professor of Information Technology at Ulyanovsk State University. Memberships in Professional Organizations: IEEE Society; IEEE Control SystemsSociety. Author of papers, monographs, and textbooks; holds patents for inventions. Field of interest: Systems and signals theory; computational mathematics. [email: kentvsem@yandex.ru]I. Semushin,
Yulia Vladimirovna Tsyganova, Ulyanovsk State University, Doctor of Science in Physics and Mathematics, Professor of Information Technology at Ulyanovsk State University. Author of papers, a monograph, and textbooks; holds State Registration Certificates of computer programs. Field of interest: Parameter identification and adaptive filtering; numerically efficient algorithms for stochastic systems. [email: tsyganovajv@gmail.com]Y. Tsyganova


Numerical Aspects of Farend Crosstalk Cancellation in Vdsl Downstream
A complexity analysis of computations involved in two precoding methods  Zero Forcing (ZF) vs. a Simplified Linear (SL)  in the context of a Very highspeed Digital Subscriber Line (VDSL) is presented in this paper. For the ZFprecoding technique, eight computing strategies have been compared, four of which entail the explicit calculation of inverse normalized channel matrices and other four do not. In addition to this analysis, SLprecoder complexity  based on the approximate matrix inversionhas been estimated. Both methods solve the problem of full or partial farend crosstalk (FEXT) cancellation in VDSL downstream transmission. For this problem, the strategy avoiding the explicit matrix inversion was found to have the smallest number of multiplication/division operations. The analysis performed provides an opportunity for VDSLdesigners to justifiably select a computationally attractive precoding strategy taking into account the necessity of adaptive power control for the input signals to the DSLchannel from the Central Station. Vdslсистемы, vdslsystems, farend channel crosstalk, downlink data transmission, zeroforcing precoding, simplified linear precoding.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Vladislav Nikolaevich Kovalnogov, Ulyanovsk State Technical University, Doctor of Science in Engineering; graduated from Kazan State University; Head of the Department of Heat Power Engineering at Ulyanovsk State Technical University; an author of articles, monographs, and inventions in the field of modeling, research and optimization of hydrogasodynamic processes in power plants and manufacturing equipment. [email: kvn@ulstu.ru]V. Kovalnogov,
Ruslan Vladimirovich Fedorov, Ulyanovsk State Technical University, Candidate of Science in Engineering; graduated from Ulyanovsk State Technical University; Associate Professor of the Department of Heat Power Engineering of UlSTU; an author of articles and inventions in the field of numerical modeling of hydrogasodynamic processes. [email: r.fedorov@ulstu.ru]R. Fedorov,
Larisa Valerievna Khakhaleva, Ulyanovsk State Technical University, Candidate of Science in Engineering; graduated from Ulyanovsk State Technical University; Associate Professor of the Department of Heat Power Engineering of UlSTU; an author of articles and inventions in the field of numerical modeling of hydrogasodynamic processes. [email: larvall@mail.ru]L. Khakhaleva,
Andrei Valentinovich Chukalin, Ulyanovsk State Technical University, graduated from Ulyanovsk State Technical University; Postgraduate Student at the Department of Heat Power Engineering of UlSTU; an author of articles and inventions in the field of numerical modeling of hydrogasodynamic processes. [email: chukalin.andrej@mail.ru]A. Chukalin


Mathematical Modeling and Numerical Analysis of Thermal Protection Effectiveness With Hemispherical Damping Cavities
The gas turbine engine performance improvement is linked inextricably with the increase of the intensity of dynamic, aeromechanical and thermal processes, which, in turn, requires the development of systems and devices allowing to protect the most loaded equipment components. The most effective ways to protect surfaces from overheating are a convective cooling; the absorption and accumulation of heat by condensed substances; the cooling that operates on mass transfer principle; the radiation and electromagnetic cooling; heatshielding coatings. One of the most effective ways to protect surfaces from overheating is a thermal protection in the form of filmlike surface cooling based on the masstransfer surfacecooling principle. This method is widely distributed and it proved to be effective. The paper considers the possibility of improving this method of cooling due to the impact on the boundary layer with hemispherical damping cavities behind the injection section of the cooler. A mathematical model is proposed, the numerical study of the thermal protection effectiveness by the use of hemispherical damping cavities is carried out. The possibility of a significant decrease of the turbulent heat exchange in the boundary layer and of the efficiency improvement of the thermal surface protection of ? by0.06 due to the use of hemispherical damping cavities has been established. The proposed method of thermal protection intensifying and numerical analysis of its efficiency will improve the gas turbine engines that are available for different applications of domestic industry for example in power generation sector, aircraft engineering as well as in shipbuilding. Hemispherical damping cavities, turbulent transport, mathematical modeling, boundary layer, thermal protection.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Albert Shamilevich Khusainov, Ulyanovsk State University, Doctor of Science in Engineering; graduated from Ulyanovsk State Technical University; Head of the Department of Design and Service of Automobile named after I.S. Antonov at Ulyanovsk State University; an author of articles, monographs, tutorials, and inventions in the field of simulating, research and optimization of tractor and vehicle constructions. [email: a.s.khusainov@gmail.com]A. Khusainov,
Andrei Anatolevich Glushchenko, Ulyanovsk State Agrarian University, Candidate of Science in Engineering; graduated from Ulyanovsk State Agrarian Institute; Associate Professor of the Departmentof Exploitation of Machineryand Mobile Technological Equipment at P.A. Stolypin Ulyanovsk State Agrarian University; an author of articles, monographs, tutorials, and inventions in the field of simulating, research and optimization of tractor and vehicle constructions. [email: oildel@yandex.ru]A. Glushchenko,
Maxim Anatolevich Volkov, Ulyanovsk State University, Candidate of Sciences in Physics and Mathematics; graduated from Ulyanovsk State University; Dean of the Faculty of Mathematics, Information and Aviation Technologies at Ulyanovsk State University; an author of articles, tutorials, and inventions in the field of the simulating and designing of complex engineering systems and the computeraided control system development. [email: volkovmax1977@gmail.com]M. Volkov


Developing the Model for Improving the Vehicles’ Operating Characteristics
The process of developing the model to improve vehicles’ operating characteristics has been described in the article. The model development is based on the interrelation and reciprocal influence of the main elements of the vehicle. Since the internal combustion engine is the source of energy and the driving force, its characteristics has a direct influence on the operating properties of the vehicle. In its turn, they mainly depend on the nature of the working process course and engine parameters. Therefore, a change in the technical and operational characteristics of the engine will entail a change in the operating characteristics of the vehicle in which it has been installed. The information model of the engine parameters’ influence on operating characteristics of the vehicle allows us to find that, for certain operating time and fixed values of operating modes, an improvement of operating characteristics of the vehicle can be made by changing the technical and operational characteristics of the engine. At the same time, considering the operating model of the internal combustion engine in a form of a specific multidimensional and multilevel system, it was found that the working process in the engine and the design parameters of its mechanisms have the greatest influence on the change in engine parameters. The main work process takes place in the engine cylinder, so the parts of the cylinderpiston group will have the greatest influence on the change in the output parameters of the engine. The use of mathematical modeling in solving this problem allows us to develop a concept of improving the vehicle’s operating characteristics, to optimize the process of choosing the ways to modernize the engine and the vehicle. Vehicle’s operating characteristics, information model, multidimensional and multilevel system.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Doctor of Science in Engineering; graduated from the Faculty of Physics of Irkutsk State University; completed his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’; an author of monographs, articles, and a manual in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov,
Vladimir Aleksandrovich Baboshin, St. Petersburg National Guard Forces Command Military Institute, Candidate of Sciences in Engineering, Associate Professor; graduated from Ulyanovsk Higher Military Command College of Communications; Associate Professor at the Department of Informatics and Mathematics of St. Petersburg National Guard Forces Command Military Institute; an author of articles and inventions in the field of the analysis and synthesis of information systems and mathematical modeling. [email: boboberst@mail.ru]V. Baboshin


Optimal Creation of Control Loops
The creation process of control loops in a hierarchical automated control system is determined by a threedimensional task of optimal distribution of control objects, monitoring software, and environment objects. Different variations of control loops are presented. An algorithm of random searching the optimal distribution of twodimensional task with control objects and environment objects is described. The analytical approximation of algorithm is given. It was obtained by the orthogonal transformation and was implemented while planning the control objects usage with regard to changing their location in space. Based on the algorithm of the twodimensional task distribution, the algorithm of random searching the optimal distribution of threedimensional task for one of the variations when each loop was created by the specified elements that are not included in other loops was developed. Following the results of the undertaken analysis, it was found that task time at high dimensionality could not comply with the dynamic of situation changing. The way of applying the analytical dependence for task time reducing is shown as well as the corresponding algorithm is described. The findings of experimental studies carried out by the use of the developed software are given. The obtained results verify the theory. Control loop, distribution task, mathematical model, solution algorithm, analytical dependence.



Sections: Automated control systems
Subjects: Automated control systems, Mathematical modeling. 
Aleksandr Nikolaevich Piftankin, FRPC JSC ‘RPA ‘Mars’, Candidate of Science in Engineering; graduatedfromthe Faculty of Mathematics and Mechanics at Ulyanovsk State University; Chief Specialist of FRPC JSC ‘RPA ‘Mars’; an author of papers in the field of process automation of complex radar information processing. [email: mars@mv.ru]A. Piftankin,
Anastasiia Vladimirovna Polovinkina, FRPC JSC ‘RPA ‘Mars’, Candidate of Science in Physics and Mathematics; graduated from the Faculty of Mathematics and Information Technologies at Ulyanovsk State University; Software Engineer at FRPC JSC ‘RPA ‘Mars’; an author of papers in the field of fundamental investigations. [email: mars@mv.ru]A. Polovinkina,
Stanislav Vladimirovich Tokmakov, FRPC JSC ‘RPA ‘Mars’, graduated from the Faculty of Mathematics, Information and Aeronautical Technologies at Ulyanovsk State University; Software Engineer at FRPC JSC ‘RPA ‘Mars’; his research interests include machine learning methods of control systems. [email: mars@mv.ru]S. Tokmakov


Mathematical Model and Algorithm for the Identification Task of Radio Emitting Objects of Tactical Situation on Data From Ships of Task Force
The article presents a mathematical model and algorithm for tasks of radioemitting objects identification. The identification task partition into component parts is carried out. New approaches to the calculation of the radioemitting object identification level from geometric and signal features will be found in the article. Authors propose a priority sequence of tasks to be solved based on practice of working with special information. A new mathematical model for constructing the identification evaluation function from signal features is developed. This model is not restricted to the assumption of thelinearity of this function. Algorithms for calculating the threshold values of object identification are presented. An algorithm for the radio object identification is developed under conditions of the computing experiment performed in the MATLAB environment. Following the results of the computing experiment, the algorithm has been defined more exactly, the positive outcomes of using the model have been provided. Passive radio aids, information identification, object identification level, machine learning method.



Sections: Automated control systems
Subjects: Automated control systems, Mathematical modeling, Architecture of ship's system. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Doctor of Science in Engineering; graduated from the Faculty of Physics of Irkutsk State University; completed his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’; an author of monographs, articles, and a manual in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


Distribution Laws of Stochastic Data Volumes on Hierarchical System Objects
The article determines analytical dependences of information resource volumes on objects of the hierarchical control system from initial data volumes incoming to the system. The article considers the following variants such as control when initial data is executive orders from an object of high level; and situation data acquisition and analyzing when initial data comes from an object of low level. It is assumed output data volume at each level to be proportional to input data volume. The calculation procedures of distribution laws and numerical characteristics of stochastic data volumes of all objects at known distribution laws of initial data and random conversion ratio of input data into output data are specified. A simulation model of the hierarchical system is created which allows to obtain distribution functions and probability density of stochastic data volumes of all objects based on known numerical characteristics of the initial data. The simulation results are presented that demonstrate the principle possibility of obtaining distribution laws and their approximation by the normal law. Hierarchical systems, stochastic variables, distribution law, simulating modeling.



Sections: Mathematical modeling
Subjects: Mathematical modeling, Automated control systems. 
Andrei Evgenievich Kukin, FRPC JSC ‘RPA ‘Mars’, Postgraduate Student of the Department of Telecommunication Technologies and Networks of Ulyanovsk State University; graduated from the Information Technology Department of UlSU; Software Engineer of FRPC JSC ‘RPA ‘Mars’; an author of articles in the field of software development for automated command and control systems. [email: mars@mv.ru]A. Kukin,
Aleksandr Nikolaevich Piftankin, FRPC JSC ‘RPA ‘Mars’, Candidate of Science in Engineering, ; graduated from the Faculty of Mechanics and Mathematics at UlSU; Chief Specialist of FRPC JSC ‘RPA ‘Mars’; an author of articles in the field of automation of fighter aircraft control and action planning. [email: mars@mv.ru]A. Piftankin,
Aleksandr Sergeevich Gutorov, FRPC JSC ‘RPA ‘Mars’, Candidate of Science in Engineering; graduated from the Faculty of Radioengineering of Ulyanovsk State Technical University; Chief Designer of FRPC JSC ‘RPA ‘Mars’; an author of articles in the field of statistical methods for signal processing. [email: mars@mv.ru]A. Gutorov,
Aleksandr Aleksandrovich Lushnikov, FRPC JSC ‘RPA ‘Mars’, Postgraduate Student of Ulyanovsk Civil Aviation Institute named after Air Chief Marshal B.P. Bugaev; graduated from the Faculty of Radioengineering of Ulyanovsk State Technical University; Deputy Chief Designer of FRPC JSC ‘RPA ‘Mars’; an author of articles in the field flight operation safety and automatic flight and traction control of aircraft. [email: a.lushnikov@mail.ru]A. Lushnikov


The Model for Forming the Flight Profile of an Aircraft Using Dynamic Programming Tools
The article deals with the process of forming the flight profile of an aircraft. Calculation and selection of the optimal flight profile of aircraft are some of the most common issues in the tasks related to the planning of aviation operations. The flight profile in the coordinates ‘rangealtitude’ is a sequence of areas each of which corresponds to a specific program for changing altitude and speed. The construction of the flight trajectory of an aircraft is characterized by the work with a large number of nonlinearly varying dependent parameters and taking into account the restrictions imposed on flights: the permitted echelons of aviation flight altitudes, forbidden zones with unacceptable meteorological conditions, forbidden zones of action of enemy air defenses. These factors make it very difficult to model the specified process. The application of the mathematical apparatus of dynamic programming in solving this problem can allow the most efficient choice of flight modes of aircraft and optimize the process of forming the flight profile as a whole. Fighter aircrafts, flight profile, optimization algorithm, dynamic programming.



Sections: Mathematical modeling
Subjects: Mathematical modeling, Architecture of ship's system. 
Oleg Vladimirovich Saverkin, FRPC JSC ‘RPA ‘Mars’, graduated from the Faculty of Radioengineering of Ulyanovsk State Technical University with the specialty in Telecommunications Networks and Connecting Systems; Postgraduate Student of UlSTU, Research Engineer of FRPC JSC ‘RPA ‘Mars’; an author of articles in the field of statistical signal processing. [email: saverkinoleg@mail.ru]O. Saverkin


On the Efficiency of Trajectory Filtering in Fixed Coordinate System
The article presents the analysis results of algorithms for estimating the motion parameters of the accompanying objects based on the application of the Kalman filter. It is shown that the application of some known algorithms is associated with the need to perform complex mathematical operations, and under certain conditions can lead to significant errors. It is established that the use of filtering in fixed coordinate system in the algorithm allows taking into account data on the direction and maneuvering of the object thereby increasing the accuracy and tracking stability. At the same time, simplicity of implementation is preserved when using the linear Kalman filter. Object tracking, trajectory parameters estimation, fixed coordinate system, kalman filter.



Sections: Mathematical modeling
Subjects: Mathematical modeling, Architecture of ship's system. 
Ilia Vladimirovich Zhuikov, Volga State University of Technology, Postgraduate Student; graduated from the Department of Applied Mathematics and Information Technologies of Volga State University of Technology; an author of articles in the field of intelligent test systems. [email: zhuikill@yandex.ru]I. Zhuikov,
Igor Nikolaevich Nekhaev, Volga State University of Technology, Candidate of Science in Engineering, Associate Professor of the Department of Applied Mathematics and Information Technologies of Volga State University of Technology, Head of the eLearning Center of Volga State University of Technology; an author of scientific papers in the field of soft computing, fuzzy logic, and elearning. [email: nehaevin@volgatech.net]I. Nekhaev


Application of Lpstructures When Constructing the Intelligent Test System
Tasks of competence level are complex tasks for solving which is not enough only knowledge, so learning and testing systems should be able to simulate structures of gradually complicating tasks. In some cases, these structures can be modeled using mathematical lattices describing the structure of cases with additional attitude of complication. This article describes a model of the lattice of noncomplication of cases for the subject domain. A method for specifying and constructing such lattice using finite LPstructures and applying operations of transitive closure on the lattice of clarification of case situations is proposed. In conclusion, the example of using this approach to construct intelligent test system of the ability to perform solve tasks of comparing numbers from the domain of arithmetic of natural numbers is considered. It is shown that this approach could be used for further analyzing the results of solutions and to construct a more pragmatic lattice of complication of cases and test tasks. Lpструктура, competencybased approach, intelligent test system, lattice of complication of cases, lpstructure.



Sections: Information systems
Subjects: Information systems, Mathematical modeling, Artificial intelligence. 
Mikhail Konstantinovich Samokhvalov, Ulyanovsk State Technical University, Doctor of Sciences in Physics and Mathematics, Professor; graduated from the Faculty of Physics of Saratov State University named after N.G. Chernyshevsky; Professor of the Department of Electronic Instrumentation Design and Technology at Ulyanovsk State Technical University; an author of articles and monographs in the field of optoelectronics. [email: sam@ulstu.ru]M. Samokhvalov


Modeling the Brightness Dynamics of Thinfilm Electroluminescent Capacitors
The processes of excitation of luminescence of thinfilm electroluminescent capacitors within the model of direct shock excitation of activator centers in the luminophore are analyzed. Mathematical modeling of the dynamics of the brightness of radiation sources is carried out on the basis of the solution of the nonlinear ordinary differential equation describing the kinetics of changes in the density of excited centers of luminescence in the phosphor film. A program for numerical solution of nonlinear equation of luminance dynamics by RungeKutt method using a computer is developed. It is shown that the duration of transient processes determined by the brightness waves reaches 810 periods of applied alternating voltage. In order to obtain high brightness levels of electroluminescent indicators, it is necessary to excite the indicator elements with suites of alternating voltage pulses, the duration of which must be at least the time of reaching the steadystate operation. Thin film electroluminescent capacitor, brightness, phosphor, electroluminescence, indicator.



Sections: Electrical engineering and electronics
Subjects: Electrical engineering and electronics, Mathematical modeling, Information systems. 
Rudolf Aleksandrovich Brazhe, Ulyanovsk State Technical University, Doctor of Sciences in Physics and Mathematics, Professor, Head of the Department of Physics at Ulyanovsk State Technical University; graduated from the Faculty of Physics of Saratov State University named after N.G. Chernyshevsky; an author of numerous scientific papers, monographs, tutorials, and invention certificates; has research interests in the field of wave processes, meta and nanomaterials, nanoelectronics, and control system elements [email: brazhe@ulstu.ru]R. Brazhe,
Andrei Fedorovich Savin, RITG, LLC, graduated from the Faculty of Physics and Mathematics of Ulyanovsk State Teachers University named after I.N. Ulyanov; Lead Analyzer of RITG, LLC; an author of publications in the field of mathematical modeling of nanoscale radioengineering components. [email: a_f_savin@mail.ru]A. Savin


Electric Characteristics of Sensing Elements of Resonance Nanosensors for Robotic Systems Based on Spiral Nanotubes
Sensing devices of nanosensors for robotic and biorobotic systems based on separate spiral nanotubes draw an attention of researchers both as from the point of view of opportunities of their design with the use of the temporary nanotechnologies as from the point of view of their high sensitivity to external influences. Owing to deformation of nanocoil as a result of external influence, its impedance changes, and a shift of a resonant frequency appears. It is shown that the resonant frequency of such nanosolenoids can reach tens petahertz, and its shift can make the tenth shares of petahertz as a result of nanocoil’s length change for 1 percent. Spiral nanotubes, resonant nanosensors, impedance properties.



Sections: Electrical engineering and electronics
Subjects: Electrical engineering and electronics, Mathematical modeling. 
Rudolf Aleksandrovich Brazhe, Ulyanovsk State Technical University, Doctor of Sciences in Physics and Mathematics, Professor, Head of the Department of Physics at Ulyanovsk State Technical University; graduated from the Faculty of Physics of Saratov State University named after N.G. Chernyshevsky; an author of numerous scientific papers, monographs, tutorials, and invention certificates; has research interests in the field of wave processes, meta and nanomaterials, nanoelectronics, and control system elements. [email: brazhe@ulstu.ru]R. Brazhe


Mechanical Characteristics of Electromechanical Resonators Based on Spiral Nanotubes
In electromechanical resonators shaped as spiral nanotubes, two types of resonances such as an electrical resonance like in serial RLC circuit and the mechanical one like in a coil spring can exist. Both types of resonances can be used for designing the sensing devices of resonance nanosensors for robotic and biorobotic systems though their resonant frequencies strongly differ from each other. This paper deals with a comparison of electrical and mechanical characteristics of the electromechanical resonators based on coiled nanotubes. It is shown that the frequency of the displacement resonance in such mechanical oscillators can reach tens of gigahertz while the current resonance occurs at the frequencies reaching tens petahertz. The amplitudefrequency and phasefrequency characteristics of forced oscillations in the considered nanospirals are brought. It is shown that their mechanical figure of merit does not exceed several units and is comparable with the electrical one because of grate attenuation. Spiral nanotubes, electromechanical resonator, resonance characteristics.



Sections: Electrical engineering and electronics
Subjects: Electrical engineering and electronics, Mathematical modeling. 
Innokentiy Vasilyevich Semushin, Ulyanovsk State University, Doctor of Science in Engineering, Professor of Information Technology at Ulyanovsk State University. Memberships in Professional Organizations: IEEE Society; IEEE Control Systems Society; “Russian Professorial Assembly”. Author of papers, monographs and textbooks; holds patents for inventions. Field of Interest: systems theory, control. [email: kentvsem@yandex.ru]I. Semushin


Towards Robust Riccati Iterations for Lqgoptimal or Parameteradaptive Estimation and Control Processes
The paper aims at the development of robust and efficient computational algorithms for stochastic linear control based on scalarized squareroot implementations. In the capacity of starting point, it uses the classical (formal) solution to the control problem known from the threedecker monography Stochastic models, estimation, and control, Academic Press, 19791982, by Peter S. Maybeck. The mutually timeinverse Riccati iterations being a core part of the solution, are interpreted in a uniform notation as the twostage update processes. For them, a transition to the two kinds of scalarized algorithms  direct and inverse, is performed to introduce into consideration a scalarized filter and scalarized regulator and avail ourselves of the opportunity to go into the question of numerically stable squareroot computation designs for Riccati iterations. The paper demonstrates one possible configuration in the form of the Potterstyle algorithm. That establishes the new direction in constructing robust LQGregulators for control as being based on many advances in robust filtering. Lqgcontrol, squareroot algorithms, finitehorizon discretetime control, scalarization.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Viacheslav Andreevich Sergeev, Ulyanovsk Branch of the Kotel’nikov Institute of Radioengineering and Electronics of the Russian Academy of sciences, Doctor of Engineering, Associate Professor; graduated from the Faculty of Physics of Gorky State Technical University; Head of Ulyanovsk Branch of the Kotel’nikov Institute of Radioengineering and Electronics (IRE) of the Russian Academy of sciences (RAS); Head of the Department of Radioengineering, Opto and Nanolectronics of Ulyanovsk State Technical University at Ulyanovsk Branch of the Kotel’nikov IRE; an author of monographs, articles, and inventions in the field of researching and simulating semiconductor device and integrated circuit performance, and measuring their thermal characteristics. [email: sva@ulstu.ru]V. Sergeev,
Sergei Evgenevich Rezchikov, Ulyanovsk Branch of the Kotel’nikov Institute of Radioengineering and Electronics of the Russian Academy of sciences, graduated from the Faculty of Radioengineering of Ulyanovsk State Technical University; Postgraduate Student of the Base Department of Radioengineering, Opto and Nanolectronics at the Kotel’nikov Institute of Radioengineering and Electronics (IRE) of RAS; an author of articles in the field of measurement automation and noise characteristics research of semiconductor devices and integrated circuits. [email: s.rezchikov@ulstu.ru]S. Rezchikov


The Optimization of Procedures for Measuring the Semiconducter Devices’ Paramters of Lowfreqency Noise Influenced By White Noise
The brief analysis of techniques for measuring the parameters of lowfrequency (LF) noise with 1/f?type spectrum has been proposed. The estimation of measurement error of power spectral density (PSD) and ?rays spectrum index are given by taking into account the influence of whitenoise level. Based on the results of noise spectral power density measurements implemented at three frequencies when series and parallel filtering, authors propose procedures of measuring the index of ?rays spectrum that minimize a total inaccuracy of ? value determination. The essence of optimization in case of serial filtering reduces to the optimum distribution of preset overall measurement time between measurements at the first, second and additional frequencies in case of the given frequency ratio, and when parallel filtering, to the determination of the optimum frequency ratio of measuring the noise PSD in case of the preset overall measurement time. A systematic measurement error of ? value has been estimated while implementing of various measurement procedures depending on ? value. The estimations are presented in the article. It is shown that the optimization of measuring procedures allows to reduce an error of the ? value determination by 1.5 to 2 times. Lowfrequency noise, power spectral density, index of spectrum form, measurement, error, optimum procedures.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Iurii Dmitrievich Ukraintsev, Ulyanovsk State University, Candidate of Engineering; graduated from the Faculty of Radiocommunications of the Leningrad Military Academy of Communications; Associate Professor of the Department of Telecommunication Technologies and Networks at Ulyanovsk State University; an author of articles, monographs inventions in the field of statistical analysis and synthesis of telecommunication systems. [email: 9019471930@mail.ru]I. Ukraintsev,
Vladimir Viktorovich Kalnikov, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Candidate of Engineering, Associate Professor; graduated from Radioengineering Faculty of Kiev Higher Military Engineering College of Communications; Chief Specialist at FRPC JSC ‘RPA ‘Mars’; specializes in the field of specialpurpose control system design, creation of communication and data exchange systems; an author of articles and inventions in the field of designing the distributed control systems of specialpurpose, communication and data exchange systems. [email: mars@mv.ru]V. Kalnikov


An Alternate Bayesian Approach to the Detection of an Adaptive Decision Threshold Scheme for the Receiver At Decameter Radio Links
The article deals with an approach to the determination of the decision threshold scheme of a receiving device in decameter radio link, which implements the alternative Bayesian method. In contrast to the classical approach when the decision threshold scheme is determined with the assumption that the probability density function (PDF) of the received signal is subject to the Gaussian low, an approach based on the current recovery of instantaneous values of the received signal envelope in each distribution path is proposed. The PDF recovery algorithm is based on the nonparametric ParzenRosenblatt density estimation method. The estimating is carried out during a specified communication session. In this case, the most probable values of the signal (mode) are determined if the noise interference is absent and present, the decision threshold scheme is established in accordance with the real situation on the communication line. Then, on the basis of the mode shift, a decision is made about the signalerror probability. On the basis of simulation modeling, the efficiency of the approach is shown when operating at decameter radio links working under nonparametric prior uncertainty relative to signals and interference. Signal depression, instantaneous values of the received signal envelope, parzen method of the probability density estimation, mode, decision threshold scheme of a receiving device, error probability.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Irina Aleksandrovna Sedykh, Lipetsk State Technical University, Candidate of Physics and Mathematics; graduated from the Faculty of Automation and Informatics of Lipetsk State Technical University (LSTU); Associate Professor of the Mathematics Department at Lipetsk State Technical University; an author of monographs and articles, owner of certificates of registration of the computer programs in the field of neighborhood modeling of dynamic systems. [email: sedykhirina@yandex.ru]I. Sedykh,
Evgenii Sergeevich Anikeev, Lipetsk State Technical University, graduated from the Faculty of Physics and Engineering of Lipetsk State Technical University (LSTU); Master’s Degree Student at Lipetsk State Technical University; an author of articles, owner of certificates of registration of the computer programs in the field of neighborhood modeling of dynamic systems. [email: evgenijanikeev@yandex.ru]E. Anikeev


Hierarchical Colored Time Petri Nets on the Basis of Neighborhood Models
The article describes the definition and algorithm for the operation of common labeled Petri nets. Some varieties of Petri nets such as timed, colored and colored timed Petri nets are shown. The proposed hierarchical colored Petri nets based on neighborhood models are an extension of the considered classes. The hierarchy in this system is represented by a set of positions and transitions, in each of which a neighborhood model can be embedded. The concept of a dynamic neighborhood model is also given in this paper. Adding a hierarchy allows to analyze additional properties of simulated dynamic distributed processes. For colored Petri nets with hierarchical transitions, an operation algorithm is formulated that is designed and implemented as a Java program. The peculiarity of the models under consideration is the synchronization of the operating time of the external and internal systems. In addition, the control signals of the embedded neighborhood model depend on the change in the current marking of the Petri net when a hierarchical transition occurs. An example of the functioning of a Petri net with a hierarchical transition is given. Modelling, colored timed petri net, hierarchical petri net, algorithm, neighborhood model.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Dmitrii Anatolevich Zhukov, Ulyanovsk State Technical University, graduated from the Faculty of Information System and Technologies of Ulyanovsk State Technical University; Postgraduate Student of the Department of Applied Mathematics and Computer Science; an author of proceedings in the field of the statistical methods and machine learning. [email: zh.dimka17@mail.ru]D. Zhukov,
Vladimir Nikolaevich Kliachkin, Ulyanovsk State Technical University, Doctor of Engineering; graduated from the Mechanical Faculty of Ulyanovsk Polytechnic Institute; Professor at the Department of Applied Mathematics and Informatics of Ulyanovsk State Technical University; an author of scientific papers in the field of reliability issues and statistical methods. [email: v_kl@mail.ru]V. Kliachkin


The Effect of the Control Sample Volume on the Quality of Diagnostics of the Technical Object State
He problem of predicting the serviceability of a technical object in terms of its performance is considered. The source data are the known results of the evaluation of the state of an object based on the results of the previous operation: If the specified values of controlled indicators technical system intact or defective. Such a problem can be solved by methods of machine learning, it reduces to a binary classification of the states of the object. The quality of diagnostics can significantly depend on many factors: the method of training, the correct allocation of factors characterizing the operation of the object, the volume of the sample, and others. The work studies the effect of the control sample volume on the quality of diagnosis, estimated by the number of mispredicted states using the crossvalidation method. The tests were carried out in the Matlab package, ten different training methods were used: logistic regression, support vector method, decision tree bugging, and others. It is shown that the correct choice of the proportion of the control sample can improve the diagnostic quality to 57%. Technical diagnostics, serviceability of the indicator of functioning, machine learning, control sample, crossvalidation.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Dmitrii Vladimirovich Samoilenko, Mozhaisky Military Space Academy, Candidate of Engineering; graduated from Shtemenko Krasnodar Highest Military School; Postdoctoral Student of Mozhaisky Military Space Academy; an author of articles, inventions in the field of information security, crypto code information security systems, modular arithmetic of multidimensional numerical systems. [email: 19sam@mail.ru]D. Samoilenko


Increasing of information survivability of the group of robotic engineering complexes under destructive attack of the violator
A group of robotic engineering complexes such as unmanned aerial vehicles (UAVs) operating under an intelligent jamming attack of a violator is considered. In order to meet these operating conditions, a subsystem of cryptographic code protection of information based on the aggregated application of block encryption algorithms and polynomial noiseimmune coding methods has been proposed. Further investigation disclosed that providing the subsystem under consideration with new properties ensuring the restoration of true encrypted information that is subjected to the destructive impact of the violator i.e. imitation proof as well as a regenerative process activation ensuring the integrity (restoration) of data i.e. information survivability are subsystem features. For the case of physical delivery of the information extracted by UAV complexes, it is suggested that the ensemble of storage devices onboard various UAVs with common functions be considered as a single system of storage devices with a subsystem of cryptographic code transformation of information. In this case, even the physical loss of the ith UAV grouping as a storage node does not lead to complete or partial loss of data (including distorted data) and allows initiating the procedure for their recovery. Group of unmanned aerial vehicles, cryptography, noiseimmune coding, imitation proof, information survivability, information integrity.



Sections: Mathematical modeling
Subjects: Automated control systems, Mathematical modeling. 
Aleksei Aleksandrovich Gudkov, the Marshal Budjonny Military Academy of Signal Corps, Master’s Degree; graduated from the Cherepovets Military Engineering Institute of Radioelectronics; the Marshal Budjonny Military Academy of Signal Corps; Adjunct of the Marshal Budjonny Military Academy of Signal Corps; an author of proceedings and publications in the field of an assessment of electromagnetic accessibility and calculation of structural stability of hierarchical systems. [email: gudkov_aa@rambler.ru]A. Gudkov,
Sergei Romanovich Malyshev, the Marshal Budjonny Military Academy of Signal Corps, Candidate of Engineering, Associate Professor; graduated from Mozhaisky Military Engineering Institute; Honored Inventor of the Russian Federation; Associate Professor of theMilitary Academy of communications an author of tutorials, articles and inventions in the field of modern theoretical aspects of radiomonitoring and radioengineering control. [email: malishevsr56@ya.ru]S. Malyshev,
Sergei Vasilevich Krasnov, Graduate School of Business Management Technologies of St. Petersburg Polytechnic University, Candidate of Engineering, Associate Professor; graduated from the Ulyanovsk Higher Military Command School of Communications; an adjunct of Ulyanovsk Military Engineering Communication School; Associate Professor of Graduate School of Business Management Technologies of St. Petersburg Polytechnic University; an author of more than 50 scientific works in the field of design and implementation of information systems and technologies. [email: hsm.krasnov@gmail.com]S. Krasnov


Parametric Synthesis of Radiomonitoring and Radiotechnical Control Systems Based on the Formal Approach
The task of synthesizing the radiomonitoring systems in the theory of complex systems is the task of estimating the optimality of the system or the problem of optimizing the system. The solution of the synthesis problem consists in considering a number of optimization problems, each of which characterized by the use of various optimality criteria. The diversity of radio electronic systems and the specific features of their functioning do not allow forming a unified methodology that allows the synthesis of any radiomonitoring system. In this regard, the synthesis of a particular system is an individual process. The concept of the synthesis of radiomonitoring system based on the general principles of the system approach in the synthesis of a complex system of any purpose, and, at the same time, includes a number of distinctive features due to the features of the system synthesized. The synthesis of the systems under consideration should include two stages: structural and parametric synthesis. At the first stage, indicators of results, requirements for results, criteria for assessing the quality of results are set. The second stage determines the efficiency index, the requirements for the level of efficiency, the criterion for assessing the effectiveness. Parametric synthesis, optimization, radiomonitoring system.



Sections: Mathematical modeling
Subjects: Automated control systems, Mathematical modeling. 
