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Item Creative Methods as an Obligatory Component of the Technical Specialists Education in the Post-Industrial Era(Faculty of Organization and Management at the Silesian University of Technology, Silesian Voivodeship, Poland, 2024) Molokanova, Valentyna M.; Petrenko, Vitaliy O.; Kuznetsov, Valeriy; Kuznetsov, Vitalii V.; Krol, Agnieszka; Kacprzak, Marzena; Wielewska, Izabela; Wyrzykowska, BarbaraShow more ENG: Purpose: The article's objective is formalization of the model, the main stages and creative methods of training technical specialists, the definition of features and directions for further education development in the post-industrial era. The article is aimed at revealing the nature of creativity, highlighting the essence of the functions of methods of creative activity and their importance for students of technical specialties. Design/methodology/approach: The work uses critical analysis of scientific and methodological sources, system and convergent analysis methods, generalization and systematization of practical experience. The method of convergent generalization made it possible to identify key indicators of the model of creative competencies. The conceptual model of creative competence was developed based on the results of cooperation on the frame of master's programs for the project managers training. For the practical part of research, a qualitative method was used (participant observation, individual interview, tests). Findings: The need to train technical specialists in the methods of creative search using modern technologies, which allows to achieve the effects of the intellectual potential development for the individual, the state and society, is justified. An experiment on training project managers of two Ukrainian institutes in creative technologies proved the feasibility of implementing such training. Based on the calculation of the creative competencies’ development of the first- and second-year study technical specialists, the need to add a mandatory creative component to educational programs has been determined. Implications/Recommendations: To assess the quality of training, a methodology for assessing the level of competence has been applied. This made it possible to identify a low level of some competencies and, at the stage of improving the curriculum, plan the necessary corrective actions for the development of weak components of competencies. Since project-oriented learning is used, the model is similar to the model of the classical project life cycle and will be especially useful in the implementation of innovative projects in production. The article presents a framework for teaching students creative competence, which can be used by other educational institutions. Originality/value: The review of literary sources proved that so far very little attention has been paid to the development of creative competencies in students of technical specialties, although these competencies will be the competitive advantage of a person in the competition with artificial intelligence. The model of creative competencies for the technical specialists training is presented, which is divided into four areas, which in turn are divided into four components. These areas relate to the sampling and systematization of knowledge; adaptation to user requirements; awareness and dissemination of hidden knowledge; transition to the active use of knowledge.Show more Item Implementation of Value-Oriented Project Portfolio Management for the Development of Complex System(WSGE University of Applied Sciences in Józefów, Poland, 2024) Molokanova, Valentyna M.; Kuznetsov, Vitalii V.; Kuznetsov, Valeriy; Petrenko, Vitaliy O.; Krol, Agnieszka; Ciekanowski, ZbigniewShow more ENG: The formation of a development portfolio is one of the key challenges facing any level of system. The aim of the article is to present a model of optimal value-oriented portfolio formation for the development of a complex system, taking into account mutual influence of portfolio components on each other. It analyses the method¬ology of portfolio development management of organizations, considers different approaches to forming a portfolio of projects, proposes the formation of a portfo¬lio of organization development based on the value-oriented approach, considers multi-criteria model of project selection in the organization development portfolio, taking into account the mutual influence of the components of the portfolio on each other. As the basic method of forming a portfolio of regional community develop¬ment using the value-based approach, taking into account the existing limits on the total value of the portfolio in the computable period is proposed. The problems of incomplete application of the portfolio management methodology in the system of public development management in Ukraine were reflected. The paper determined that although the project approach is increasingly used in Ukraine to manage the de¬velopment of territories, for many acute problems portfolio development management is not used. The necessity of managers training for portfolio management of regional systems development has been substantiated. Suggested the use of value-oriented methodology of project management to manage regional development, which significantly improves the quality of planning and effectiveness of the implementation of development strategy through projects.Show more Item On the Feasibility of Choosing Means of an Asynchronous Motor Protection in Industrial Conditions(ScientificWorld-NetAkhatAV, Karlsruhe, Germany, 2023) Tryputen, Mykola; Kuznetsov, Vitaliy V.Show more ENG: The article is devoted to the urgent problem of choosing the means of protection of asynchronous motors (AM) operating in the shop electric networks of industrial enterprises with low-quality electricity. The well-known energy-economic model of an induction motor is presented in the form of a predicate disjunction, to which we apply the pattern recognition algorithm for making decisions. The main advantage of the predicate model is openness and the possibility of accumulating knowledge about the operating modes of electromechanical equipment. The practical implementation of training, adaptation, minimization of the predicate model and the search on its basis for the best option for protecting an asynchronous motor in high-level algorithmic languages involves the processing of large amounts of data. It is shown that elements of predicate equations can be represented as a relational data model and use operations - algebras for its transformations. The transformation procedures are easily integrated into the information and software structures of the automated enterprise management structure, which use database management systems oriented to relational models.Show more Item Enhancing Power Quality within the Context of Industrial Enterprises: Strategies for Improvement(ScientificWorld-NetAkhatAV, Karlsruhe, Germany, 2023) Tryputen, Mykola; Kuznetsov, Vitaliy V.; Nikolenko, Anatoliy V.Show more ENG: The paper analyzes negative impact of poor-quality electricity on the performance of electrical installations. Particular attention is paid to the ways to improve power quality under the conditions of industrial enterprises. Use of “individual” LC-filters to protect extra important electric drives; use of “group” devices to compensate negative effect of noisy electricity at a workshop level (power active rectifiers are meant with their potential integration into the available converters for the controlled electric drives); and to inhibit voltage distortions within the areas of their origination (i.e. the mains protection against the root cause) are possible means to solve the problems.Show more Item Minimization of Power Fluctuations of Wind Power Plants when Constructed in Exclusion Zones of Enterprises(Dnipro University of Technology, Dnipro, Ukraine, 2023) Kachan, Yu. G.; Kuznetsov, Vitalii V.; Shram, O. A.Show more ENG: Purpose. Development of a methodology for selecting types and quantities of wind turbines built in exclusion zones of industrial enterprises to minimize fluctuations in the power generated by them and increase the efficiency of their use. Methodology. The work used methods of synthesis of systems, computer modeling in the calculation of the optimal number of different types of wind turbines, methods of combinatorics. Findings. The developed method for designing wind power plants built in the exclusion zones of enterprises allows determining the required number of different types of wind turbines with different capacities and nominal values relative to the wind speed, which will provide the necessary generated power with minimal fluctuations. This makes it possible to notably reduce the capacity required for the accumulation of excess generation and to significantly reduce the cost of implementing wind turbines. Originality. The work proposes a methodology for designing wind power plants based on various wind turbines, taking into account their type, power and wind characteristics of the area where the wind power plant is being built. It has been found that the coefficient of fluctuation of the power generated by the wind power plant built on the same type of wind turbines does not depend on the capacity of such a station, nor on the number of wind turbines used, but only on the type of the latter and the wind characteristics of the area where it was built. Practical value. Wind power plants used at enterprises have significant daily and annual fluctuations in the power generated by them. The proposed approach allows reducing fluctuations of power generated by the station, as well as increasing the amount of electricity generation in comparison with the use of the same type of wind turbines.Show more Item Mathematical Model of the Closed-Loop System of Excavator Bucket Positioning(Dnipro University of Technology, Dnipro, Ukraine, 2023) Tytiuk, V.; Chornyi, O.; Mrachkovskyi, D.; Tryputen, S.; Tryputen, M.; Kuznetsov, Vitalii V.Show more ENG: Purpose. Study on energy consumption of mechatronic systems of mining excavators during the full production cycle, development of energy efficiency criterium for the production cycle of mining excavators, which ensures an increase in the technical and economic indicators of the operation of powerful mining equipment. Methodology. Mathematical modeling of electro-mechanical system of “front shovel” excavator, determination indicators of the production cycle, development of the criterion of energy efficiency of the mining excavator’s operating cycle taking into account the theory of technical systems efficiency. Findings. A mathematical model of a complete electro-mechanical system of an excavator with “generator-engine” electric drive has been developed, which includes a model of the mechanical part of the excavator. The closed-loop bucket positioning system makes it possible to implement various movement trajectories during the operating cycle. Numerical characteristics of energy consumption and duration for various movement trajectories of the working bodies of the excavator are obtained. A new criterion of energy efficiency of mechatronic systems of mining excavators is proposed. Originality. For the first time, a mathematical model has been proposed of an integral electro-mechanical system of an excavator according to the “front shovel” scheme, which includes models of electric drives of all mechanisms and a synchronous drive motor, as well as a model of the mechanical part of the excavator; this makes it possible to increase the accuracy of determining the excavator’s energy consumption and the operating cycle time. A criterion of energy efficiency is proposed, which takes into account the amount of resource costs, the overall result and the duration of the excavator’s operating cycle. Practical value. A mathematical model of the electromechanical system of an excavator with an electric drive according to the “generator-motor” system has been developed, which, taking into account the solution of the direct and inverse problems of the kinematics of the mechanical system of the excavator, makes it possible to compare parameters of various trajectories of movement of the excavator. The implementation of a closed system for positioning the excavator bucket in three-dimensional space was proposed, which creates conditions for increasing the level of automation of mining excavators. A criterion of the energy efficiency of the excavator’s technological cycle is proposed, which takes into account resource costs and the technological cycle duration.Show more Item Mathematical Model of a Three-Phase Induction Motor with Asymmetrical Twelve-Zone Stator Windings(IEEE, 2022) Tytiuk, Valerii; Chornyi, Oleksii; Busher, Victor; Siverskaya, Tatyana; Baranovskaya, Mila; Kuznetsov, Vitalii V.Show more ENG: The paper proposes a mathematical model of a three-phase induction motor with an asymmetrical twelve-zone winding of stator with parallel connection of subwindings. The mathematical model was developed using the theory of generalized electromechanical converter and contains equations of electrical equilibrium of six stator windings and three rotor windings. The equations for calculating the electromagnetic moment and the equations of motion of the induction motor with an asymmetrical twelve-zone stator winding rotor were obtained. The developed mathematical model in the form of cell-matrix equations has been implemented in MATLAB/Simulink.Show more Item Nonlinear Analysis of Bifurcatory Properties of Mathematical Model of Subpopulation Dynamics in the Case of a Single Niche for Subpopulation(IEEE, 2022) Kuzenkov, Olexandr; Busher, Victor; Chornyi, Oleksii; Nikolenko, Anatoliy V.; Kuznetsov, Vitaliy V.; Savvin, Oleksandr V.Show more ENG: The article is devoted to the use of mathematical models of the dynamics of heterogeneous populations, and computer simulation based on the above models allows to identify general trends in subpopulations, predict the state of the system and obtain results on possible consequences of artificial intervention. Also, the use of mathematical models can predict the spread of genetic anomalies. The authors propose a model of subpopulation dynamics with a logistic function as a basic one. It is concluded that the system-wide dynamics of subpopulation processes depends not only on the reproductive potential of subpopulations, but also on the intrasystemic dynamics that objectively occur in such systems. The adequacy of the proposed mathematical model is proved. © 2022 IEEE.Show more Item Methods of Pulse Width Modulation in Cascaded High Voltage Frequency Converters(IEEE, 2022) Busher, Victor; Chornyi, Oleksii; Tytiuk, Valerii; Glazeva, Oksana; Rozlutskyi, Oleksandr; Kuznetsov, Vitaliy V.Show more ENG: Purpose. The aim of this work is to compare the effectiveness of various methods for correcting cell failures in cascade high voltage frequency converters. These methods provide the smallest voltage drop on the motor, the least loads and oscillation of electromagnetic torque in an accident modes, and evaluate the effectiveness of pulse width modulation (PWM) methods with the injection of third harmonic and space-vector PWM in normal and emergency modes. Methodology. We use mathematical and geometrical interpretation of all analysed methods - Sinusoidal PWM (SPWM), Balanced sinusoidal PWM (BSPWM), Balanced PWM with injected 3rd harmonic (THPWM) and Balanced Space Vector PWM (SVPWM). Results. The method of balancing the phase-to-phase voltages by to such a shift of the zero point and rotation of the phase vectors, in which the amplitude of the phase-to-phase voltage decreases to the minimum possible value. Injection of the 3rd harmonic allows you to further increase the utilisation factor of power supplies in terms of voltage. But the violation of the symmetry of the phase voltages leads to the need to reduce the voltage amplitude to exclude saturation of the power supplies, which reduces this coefficient compared to the theoretically possible 15.6%. A distinctive feature of the method of balanced Space Vector PWM is that the amplitude of the 1st harmonic is always greater than the radius of the circle by 15.6%. Comparison of methods of space vector PWM (SVPWM), balancing of phase-to-phase voltage with the injection of the 3rd harmonic (THPWM) with sinusoidal PWM shows that SVPWM is the best method. Despite the more complex mathematical software for the implementation of this method, it provides the best performance in all considered emergency modes of 3...6 cascade converters. The Table of indicators for all methods are presented in the article. The use of a balanced SVPWM in combination with field oriented control makes it possible to obtain an electric drive in which, in the event of an accident, there are practically no shock mechanical and electromagnetic processes. After damage of cells the currents, electromagnetic torque and motor speed change along the required trajectory. © 2022 IEEE.Show more Item Analysis of Operational Characteristics of SRM in Emergency Modes of the Converter Unit(IEEE, 2022) Vlasenko, Vladimir; Tytiuk, Valerii; Kuznetsov, Vitalii V.; Kuntush, Yelena; Chornyi, Oleksii; Busher, VictorShow more ENG: The paper analyzes the issues of maintaining the operability of a switched reluctance motor (SRM) in various emergency situations. The researches were carried out using simulation modeling in the Matlab environment, the developed model was used for both normal and emergency operation modes. A series of dynamic tests of the motor torque has been carried out, and the values of the electromagnetic torque pulsation coefficient have been calculated. The possibility of maintaining the operability of SRM in the event of various emergency situations in the phases of the motor has been proved. The static mechanical characteristics of the motor are built and the calculation of the droop of the mechanical characteristics for possible emergency modes is performed. © 2022 IEEE.Show more Item Study of Short Circuit Currents in a Distributed Traction Power Supply System with Renewable Electric Power Sources(IEEE, 2022) Kuznetsov, Valeriy; Kuznetsov, Vitaliy V.; Bondar, Oleh I.; Rojek, Artur; Hubskyi, Petro; Stypulkowski, PiotrShow more ENG: The problems of changing short-circuit currents in a distributed traction system for using renewable energy sources were analyzed in the article. Literary sources analysis shows a further tendency for increasing the share of renewable energy sources in the total energy balance of the country and a particular increase in electricity consumption by electric traction. Goal. The main goal of the study is a method development with its practical application to impact estimation of power-boost points that connected to the traction network with energy using from renewable sources on short-circuit currents values. Methodology. The method that has developed in this study is based on well-known approaches for equivalent circuits of electrical equipment definition, but elemenst pair like «solar panel - inverter» it reproduces as EMF with equivalent resistance, which significantly simplifies further calculations. Results. The study results show that the application of power-boost points will not lead to a significant increase of short-circuit currents in the traction network even if the power of photovoltaic sources will be comparable with the power of existing converting units on traction substations. This is because of the physical nature of the photovoltaic panel and its power mode which usually closer to the current source with high internal resistance. Practical value. This also allows us to conclude that in most cases from the point of view of changing the short circuit currents the integration of power-boost points that are powered by solar power plants is quite possible with operating sections of the traction power supply system.Show more Item The Urgency of Using Adaptive Observers to Identify the Parameters of the DC Electric Drive(Springer, Cham, 2022) Stopkin, Vasyl V.; Nikolenko, Anatoliy V.; Kuznetsov, Vitaliy V.; Tryputen, Mykola; Kuzenkov, OleksandrShow more ENG: The aim of this paper is to analyze the use of surveillance devices in modern digital electric drives with the prospect of modernization of existing DC drives used in the metallurgical industry of the Dnieper region of Ukraine and develop a mathematical model of electric drive with adaptive observer identification of basic coordinates. The urgency of the work is justified, given the large number of outdated control systems for DC electric drives at metallurgical enterprises in the Dnieper region. There are even drives with a generator-DC motor system in the presence of thyristor converters in the excitation windings of motors and generators, such as a generator system – a blooming DC motor 1050 in a rolling shop №1 PJSC “Dnieper Metallurgical Plant”, a generator system – DC motor rolling shop of PJSC “Dnieper Metallurgical Plant”. There are also more modern – for example, digital system thyristor converter – DC motor of the electric drive of a calibration condition in the conditions of rolling shop №7 INTERPIPE NIKO TUBE, Nikopol. The power of the main drives is from 80 kW to 8 MW. Also, the aim of the work is to create a general classical mathematical model of the DC electric drive with observers to identify such parameters as the moment of inertia, the resistance of the armature circuit. The obtained results give an idea of the interdependence of the main parameters of the electric drive, which characterize and influence the dynamic properties of observers – the roots of the characteristic equation, structural coefficients, the frequency of undamped oscillations. The practical value includes recommendations for adjusting the control circuits for regenerative monitoring devices, the coordinates of the electric drive, which are obtained as a result of research on a mathematical model. The recommendations can be used as input, for example in the configuration of control systems, control circuits for digital complete DC electric drives in environments such as the TIA Portal Siemens before the first start-up of electric drives in the plant. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.Show more Item The Impact of Connecting a Wind Power Plant on Emergency Modes of a Traction Substation of an AC Traction System(Springer, Cham, 2022) Kachan, Yurii; Kuznetsov, Vitaliy V.; Bondar, Oleh I.Show more ENG: Among the countries of South-Eastern Europe, Ukraine has the greatest technical potential for the implementation of renewable energy sources, and the main part of it is wind power engineering. The traction power supply system of the railways in Ukraine can become an important transiter and consumer of electricity generated by wind power plants. At the same time, the task of ensuring traffic safety and uninterrupted power supply of traction loads requires a preliminary study of the influence of the connected wind power plant capacity on the growing short-circuit currents in the distributive units of the traction substation to which the specified connection is planned. This paper proposes a way to implement such prediction based on a systematic approach, in which a traction substation and an integrated wind power plant are considered as a single electrical-engineering complex, the sources of which work to power the short-circuit point. In previously published studies, the authors usually consider the processes in renewable energy sources and in the traction power supply system separately, without taking into account the mutual influence. The analysis of processes in the short-circuit mode is proposed to perform according to the equivalent circuits for the specified electrical-engineering complex developed by the authors with various possible options for connecting a wind power plant using mathematical modeling with proven methods of theoretical electrical engineering. The peculiarity of the study presented in this paper is also the use of the multiplication factor of the short-circuit current as a criterion for assessing the impact of the power of the connected wind power plant on the short-circuit currents of the traction substation. In our opinion, the coefficient applied by us more clearly characterizes the specified influence in comparison with operating values or complex sizes of short-circuit currents.Show more Item Investigation of the Bifurcation Properties of the Dynamics of a Biological Population Based on a Logistic Model(Springer, Cham, 2022) Busher, Victor; Chornyi, Oleksii; Kuzenkov, Oleksandr; Tryputen, Mykola; Kuznetsov, Vitaliy V.; Rumiantsev, VladislavShow more ENG: The paper substantiates the structure of the model that describes the dynamics of subpopulations in the general ecological niche. Based on the theory of bifurcations, the results of experimental studies of the effect of excess electromagnetic radiation of worn out or repaired electromechanical equipment on biological objects are analyzed. Analysis of phenotypic changes in the biological test object of Drosophila melanogaster, identified over three generations, based on the bifurcation model, made it possible to identify trends in long-term forecasts, which are in good agreement with the known results of population development in unfavorable conditions.Show more Item Method for Determining the Generating Capacity of the Waste Heat Recovery System of Main Engines(Springer, Cham, 2022) Rak, Alexander; Busher, Victor; Glazeva, Oksana; Chornyi, Oleksii; Kachan, Yurii; Kuznetsov, Vitaliy V.Show more ENG: A study of waste heat recovery systems for robust ship power systems (tens of MW) and installations of relatively low power (1…3 MW) of diesel locomotives has been carried out. A method for calculating the power of gas and steam turbines as part of the waste heat recovery systems has been developed. Based on simple calculations for two operating points, the method allows you to get the amount of the waste heat recovery system generated energy in other modes, different from those given in the instructions for technical operation. Preference for one or another type of turbine generator or their combination should be provided based on a feasibility study, taking into account capital investments and the power of energy consumers in the vehicle, as well as long-term prospects in fuel-saving and reducing greenhouse gas emissions. The waste heat recovery system's energy characteristics can be used to confirm the compliance of the main power plant with the requirements of the MARPOL 73/78 convention in terms of improving energy efficiency design index and reducing greenhouse gas emissions at loads of 50%, 75%, 100%.Show more Item Virtual Laboratory Works in Teaching Practical Circuit Design and Development of Responsibility Component of Students’ Academic Integrity(Springer, Cham, 2022) Borodai, Valerii; Berdnyk, Lada; Kuznetsov, Vitaliy V.; Tsyplenkov, Dmytro; Havrylova, AlvinaShow more ENG: The paper deals to the study of the role of virtual laboratory in the development of students’ responsibility contributing to their academic integrity support. The aim of our paper is to describe the experience of using virtual technology for organizing of the system of laboratory works on course of Practical Circuit Design with respect to students’ responsibility development being the value of academic integrity with the research questions as follows: to determine the students’ attitude towards the use the virtual technology in the course; to observe the changes of students’ responsibility as a part of their academic integrity development. The quantitative and qualitative results enable us to prove links between the possibilities created by the assistance of virtual technology in the course of Practical Circuit Design and the implementation of student student-centered learning on the way of students’ responsibility and academic integrity support.Show more Item Development of the System of Initial Excitation of the Autonomous Induction Generator(Springer, Singapore, 2022) Chenchevoi, Volodymyr; Kuznetsov, Valeriy; Zachepa, Iurii; Chornyi, Oleksii; Chencheva, Olga; Kuznetsov, Vitaliy V.; Yatsiuk, Rostyslav; Luhova, OlhaShow more ENG: The article defines the conditions of self-excitation of an inductive generator with capacitor excitation as part of an autonomous power source. Recommendations for the design of an autonomous power source based on an asynchronous machine in terms of the implementation of self-excitation conditions and optimal operating modes are formulated. A simulation model of an autonomous inductive generator and a solar battery for the analysis of transient, static and dynamic modes of operation has been developed. The conducted theoretical studies of capacitive self-excitation of inductive machines have created a good basis for solving problems related to the practical use of autonomous sources based on an inductive generator.Show more Item Integrated Use of Photovoltaic and Wind Power Plants in Power Supply Systems(Springer, Singapore, 2022) Ostapchuk, Oleksandr; Kuznetsov, Valeriy; Bydko, Maryna; Kuznetsov, Vitaliy V.; Kuznetsova, YevheniiaShow more ENG: The use of energy from only one type of renewable energy source (e.g., solar and wind generation) leads to a significant increase in the cost of electricity supply due to the need to install a backup power source (energy storage system or power system). This phenomenon is caused by the significant dependence of these sources on weather conditions. The wind speed is less than 4 m/s for a long time in summer, and solar energy is not available at all in dark day periods, which in December can last up to 16 h. Accordingly, the effective use of such systems is possible only if constructing a complex application of several sources of different nature (solar and wind generation). This measure allows increasing their energy efficiency by 30–50%. The combined use of these types of distributed generation is accompanied by the equalization of the daily energy intake due to the spread of the annual maximums of energy intake, but the daily fluctuations remain pretty significant. As a result of the conducted researches, it is established that when using the share of solar energy at the level 0.4… 0.55 of the total amount, the shortest period of energy deficit (at the level of 8 days per year) is observed. At other ratios between the shares of solar and wind energy, the period of energy deficit will increase. In case of increased requirements for providing responsible consumers with electricity, it is advisable to use systems with buffer electricity storage. The developed mathematical models allow calculating the equipment parameters used in the construction of efficient power supply systems.Show more Item Lyapunov Function in the Hyper-Complex Phase Space(Springer, Singapore, 2022) Voliansky, Roman; Volianska, Nina; Kuznetsov, Valeriy; Sadovoi, Aleksandr; Kuznetsov, Vitaliy V.; Kuznetsova, Yevheniia; Ostapchuk, OleksandrShow more ENG: The paper deals with the development of background for defining Lyapunov functions for a wide range of linear dynamical objects. This background is based on assuming that the Lyapunov function is redundant energy in the considered object, and this energy is dissipated only during controlled motion. We assume the full derivative of the Lyapunov function for an autonomous motion of the control objects equals zero, and we use its summands to define linear algebraic equations. The solution of these equations allows us to find unknown terms of the Lyapunov function. The use of these terms, while the Lyapunov equation is being written down, shows that the left-hand expression in the Lyapunov equation is equal to the zero matrix. Thus, we avoid subjective assuming of quadratic form terms in the right-hand of the Lyapunov equation. We extend the proposed approach to the class dynamical system with uncertainty. This extension is performed by using interval methods, which allow defining object motions for minimal and maximal values of parameters. We show that for the control object, which parameters are not exactly known, one should consider two equations of object motions, which correspond to its trajectories on the boundaries of the intervals. Lyapunov functions are defined for these boundary trajectories. Since such an approach increases the number of the considered equations, we offer to decrease them by using hyper-complex numbers while object equations are written down.Show more Item The Generalized Chaotic System in the Hyper-Complex Form and Its Transformations(Springer, Cham, 2022) Voliansky, Roman; Volianska, Nina; Kuznetsov, Vitaliy V.; Tryputen, Mykola; Kuznetsova, Alisa; Tryputen, MaksymShow more ENG: The paper deals with the development of the mathematical backgrounds to design the novel chaotic systems by transforming existent ones. These backgrounds are based on using well-known shift, rotation, and scale transformations and we offer using hyper-complex numbers to simplify these transformations and represent the transformed chaotic system by using the one 1st order ordinary differential equation. In such form all well known, newly discovered and unknown chaotic systems have the similar mathematical models that are differs only by used nonlinear function of hyper complex variable in the right hand expression. That is why the consideration chaotic system dynamic in the hyper-complex domain allows us to simplify initial system definition as well without applying any transformations. This fact simplifies mathematical definition of chaotic systems and their modeling and simulation. The right-hand expression of the transformed equation in this case are defined as the combination of transformation hyper-complex numbers and source system nonlinearity which is given in the hyper-complex domain. We offer to use variable transformation factors to improve the performance of the considered chaotic system. Since the above-mentioned variable factors can be produced by other chaotic systems, we suggest designing the novel chaotic system by combining existed ones with the linear transformations. As an example, we consider the transformation of the well-known Lorenz system and show the differences between the source system and target one.Show more

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