Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.201
S. Kuptsova, S. Y. Kuptsov
The nonlinear time-delay systems are considered and the limiting Behavior of their solutions is investigated. The case in which the solutions have a trivial equilibrium that may not be an invariant set of the system is studied. The junction of Lyapunov - Krasovskii and Razumikhin approaches is applied to obtain sufficient conditions for the existence of an asymptotic quiescent position in the large. In the case when a general system has a trivial solution, new sufficient conditions for its asymptotic stability are obtained. Examples, that illustrate the application of the obtained results, are given.
{"title":"RESEARCH OF THE ASYMPTOTIC EQUILIBRIUM OF TIME-DELAY SYSTEMS BY JUNCTION OF LYAPUNOV - KRASOVSKII AND RAZUMIKHIN APPROACHES","authors":"S. Kuptsova, S. Y. Kuptsov","doi":"10.21638/11701/spbu10.2022.201","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.201","url":null,"abstract":"The nonlinear time-delay systems are considered and the limiting Behavior of their solutions is investigated. The case in which the solutions have a trivial equilibrium that may not be an invariant set of the system is studied. The junction of Lyapunov - Krasovskii and Razumikhin approaches is applied to obtain sufficient conditions for the existence of an asymptotic quiescent position in the large. In the case when a general system has a trivial solution, new sufficient conditions for its asymptotic stability are obtained. Examples, that illustrate the application of the obtained results, are given.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"32 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86752320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.116
D. Qi, V. Bure
This study is devoted to the application of methods of applied statistics to the study of investment attractiveness of regions of China. Methods of applied statistics are widely used in various engineering research, medicine, economics, sociology, astronomy, ecology, physics, information technology, etc. statistical tools is an integral part of the study. Data taken from the World Bank website and the China Statistical Yearbook. The main topic of this research is: What factors are most strongly associated with investment attractiveness in the economy of modern China? Such a study can only be carried out based on the analysis of economic data, especially in the conditions of the modern digital economy. Consequently, the problem under consideration belongs to the field of applied mathematics. First of all, need to choose a mathematical model and research method. This paper uses the method of regression analysis - one of the most important methods for analyzing economic data. Regression models are mathematical models built from empirical data. Observations (empirical data) are the numerical data on the level of investment in the regions of China, as well as the numerical values of various factors. For each year, a multiple regression model is built using the least squares method, its statistical significance is checked, statistically significant factors are selected (statistically significant coefficients for the factors correspond to them). Calculations are carried out in Excel and SPSS, using subroutines and. Mathematical functions, but at the same time, an algorithm for analyzing the initial data based on a stepwise regression algorithm has been developed, in which only one factor with the least significant coefficient (maximum p-value (t)) is discarded at each step and then an algorithm for choosing the most important factors for investment attractiveness was developed, the essence of this algorithm is that the regression models are compared for each year and how many times each factor was included in the model is calculated algorithms can be attributed to the application of methods informatics in this work. The choice of the most important factors that determine the level of investment attractiveness is made to solve the problem of managing the economy. Attracting investments is important for the effective development of every region, every city, every district. With the receipt of significant investments, it is possible to solve the problems of economic and social development. Determination of the most important factors will make it possible to most effectively solve the problem of managing the economic development of each region, each city, each district.
{"title":"Statistical analysis of investment attractiveness of China’s regions","authors":"D. Qi, V. Bure","doi":"10.21638/11701/spbu10.2022.116","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.116","url":null,"abstract":"This study is devoted to the application of methods of applied statistics to the study of investment attractiveness of regions of China. Methods of applied statistics are widely used in various engineering research, medicine, economics, sociology, astronomy, ecology, physics, information technology, etc. statistical tools is an integral part of the study. Data taken from the World Bank website and the China Statistical Yearbook. The main topic of this research is: What factors are most strongly associated with investment attractiveness in the economy of modern China? Such a study can only be carried out based on the analysis of economic data, especially in the conditions of the modern digital economy. Consequently, the problem under consideration belongs to the field of applied mathematics. First of all, need to choose a mathematical model and research method. This paper uses the method of regression analysis - one of the most important methods for analyzing economic data. Regression models are mathematical models built from empirical data. Observations (empirical data) are the numerical data on the level of investment in the regions of China, as well as the numerical values of various factors. For each year, a multiple regression model is built using the least squares method, its statistical significance is checked, statistically significant factors are selected (statistically significant coefficients for the factors correspond to them). Calculations are carried out in Excel and SPSS, using subroutines and. Mathematical functions, but at the same time, an algorithm for analyzing the initial data based on a stepwise regression algorithm has been developed, in which only one factor with the least significant coefficient (maximum p-value (t)) is discarded at each step and then an algorithm for choosing the most important factors for investment attractiveness was developed, the essence of this algorithm is that the regression models are compared for each year and how many times each factor was included in the model is calculated algorithms can be attributed to the application of methods informatics in this work. The choice of the most important factors that determine the level of investment attractiveness is made to solve the problem of managing the economy. Attracting investments is important for the effective development of every region, every city, every district. With the receipt of significant investments, it is possible to solve the problems of economic and social development. Determination of the most important factors will make it possible to most effectively solve the problem of managing the economic development of each region, each city, each district.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"21 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86093350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.111
A. Y. Markelova, Alexander Allahverdyan, Alexey A. Martemyanov, Inga Sokolova, O. Petrosian, Mikhail V. Svirkin
More and more experts agree that in the near future, most freight traffic will be carried out using automated systems, and of them drone delivery is considered to be the most promising. Drone delivery would benefit by independence from the limitations of transport infrastructure and road conditions and would ensure cargo delivery with rapid turnaround times, as well as a significant reduction of environmental impact. The technical capabilities of unmanned aerial vehicles improve year by year, so the task of coordinating drones and effectively planning routes is relevant and in great demand. The development of such technologies will help reduce transportation costs and improve customer service through faster delivery. This article discusses the applied routing problem for a fleet of drones with limited load capacity for the delivery of heterogeneous goods with the possibility of loading in multiple warehouses from an international optimization competition. The solution includes new approach based on a mixed dimensional parallel genetic algorithm (MDPGA) for finding rational routes for delivering goods to various customers and an assignment problem to reduce the dimension depending on the number of warehouses.
{"title":"Applied routing problem for a fleet of delivery drones using a modified parallel genetic algorithm","authors":"A. Y. Markelova, Alexander Allahverdyan, Alexey A. Martemyanov, Inga Sokolova, O. Petrosian, Mikhail V. Svirkin","doi":"10.21638/11701/spbu10.2022.111","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.111","url":null,"abstract":"More and more experts agree that in the near future, most freight traffic will be carried out using automated systems, and of them drone delivery is considered to be the most promising. Drone delivery would benefit by independence from the limitations of transport infrastructure and road conditions and would ensure cargo delivery with rapid turnaround times, as well as a significant reduction of environmental impact. The technical capabilities of unmanned aerial vehicles improve year by year, so the task of coordinating drones and effectively planning routes is relevant and in great demand. The development of such technologies will help reduce transportation costs and improve customer service through faster delivery. This article discusses the applied routing problem for a fleet of drones with limited load capacity for the delivery of heterogeneous goods with the possibility of loading in multiple warehouses from an international optimization competition. The solution includes new approach based on a mixed dimensional parallel genetic algorithm (MDPGA) for finding rational routes for delivering goods to various customers and an assignment problem to reduce the dimension depending on the number of warehouses.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"19 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78167502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.406
Yang He, D. Qi, V. Bure
In this paper, we propose an econometric model based on the multiple linear regression method. This research aims to evaluate the most important factors of the dependent variable. To be more specific, we consider the properties of this model, model quality, parameters test, checking the residual of the model. Then, to ensure that the prediction model is optimal, we use the backward elimination stepwise regression method to get the final model. At the same time, we also need to check the properties in each step. Finally, the results are illustrated by a real case in China air quality. The achieved model was applied to predict the 31 capital cities in Сhina's air quality index (AQI) during 2013-2019 per year. All calculations and tests were achieved by using R-studio. The dependent variable is the China's AQI. The control variables are six pollutant factors and four meteorological factors. In summary, the model shows that the most significant influencing factor of the AQI in China is PM2.5, followed by O3.
{"title":"New application of multiple linear regression method - A case in China air quality","authors":"Yang He, D. Qi, V. Bure","doi":"10.21638/11701/spbu10.2022.406","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.406","url":null,"abstract":"In this paper, we propose an econometric model based on the multiple linear regression method. This research aims to evaluate the most important factors of the dependent variable. To be more specific, we consider the properties of this model, model quality, parameters test, checking the residual of the model. Then, to ensure that the prediction model is optimal, we use the backward elimination stepwise regression method to get the final model. At the same time, we also need to check the properties in each step. Finally, the results are illustrated by a real case in China air quality. The achieved model was applied to predict the 31 capital cities in Сhina's air quality index (AQI) during 2013-2019 per year. All calculations and tests were achieved by using R-studio. The dependent variable is the China's AQI. The control variables are six pollutant factors and four meteorological factors. In summary, the model shows that the most significant influencing factor of the AQI in China is PM2.5, followed by O3.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"36 23","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72372206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.105
V. Mazalov, V. Khitraya, Andrei V. Khitryi
A method of ranking the corpus of texts of a news portal, based on measures of graph centrality, is proposed. Each text is assigned a vertex of a certain graph, and its structure is determined based on the semantic connectivity of the texts. As a measure of centrality, the Myerson value is used in a cooperative game on a graph, where the number of simple paths in a subgraph of a certain length m is chosen as a characteristic function For different values of m, the ranking based on the Myerson value will be different. For the final ranking, it is proposed to use the ranking procedure based on the tournament matrix. The operation of the ranking algorithm is illustrated by numerical examples related to a specific news porta.
{"title":"Cooperative game theory methods for text ranking","authors":"V. Mazalov, V. Khitraya, Andrei V. Khitryi","doi":"10.21638/11701/spbu10.2022.105","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.105","url":null,"abstract":"A method of ranking the corpus of texts of a news portal, based on measures of graph centrality, is proposed. Each text is assigned a vertex of a certain graph, and its structure is determined based on the semantic connectivity of the texts. As a measure of centrality, the Myerson value is used in a cooperative game on a graph, where the number of simple paths in a subgraph of a certain length m is chosen as a characteristic function For different values of m, the ranking based on the Myerson value will be different. For the final ranking, it is proposed to use the ranking procedure based on the tournament matrix. The operation of the ranking algorithm is illustrated by numerical examples related to a specific news porta.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"24 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90199454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.413
V. V. Yevstafyeva, A. M. Kamachkin, D. Potapov
We consider an automatic control system with a three-position hysteresis relay and a continuous periodic external perturbation. The existence theorem is established that provide domains in the space of system parameters, including the parameters of the relay and perturbation, to which periodic modes having a pass to saturation zones with given periods and a specified configuration of phase trajectories correspond.
{"title":"Periodic modes in an automatic control system with a three-position hysteresis relay","authors":"V. V. Yevstafyeva, A. M. Kamachkin, D. Potapov","doi":"10.21638/11701/spbu10.2022.413","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.413","url":null,"abstract":"We consider an automatic control system with a three-position hysteresis relay and a continuous periodic external perturbation. The existence theorem is established that provide domains in the space of system parameters, including the parameters of the relay and perturbation, to which periodic modes having a pass to saturation zones with given periods and a specified configuration of phase trajectories correspond.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"3 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75472203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.308
A. V. Orekhov, Yurii M. Artem’ev, G. Pavilaynen
We discuss the change in mechanical properties of polymeric nanocomposites with photoactive components caused by solar range lighting. Given degradation photoassisted processes are related with the semiconductor nature of component photoactive particles as photocatalysts. Semiconductor particles can be transferred into electron-exited states due to light quanta absorption. One possible way out from these states is through redox electrochemical reactions with neighbor molecules. The redox reactions can produce transformations of polymer structure and composition, decreasing its mechanical strength. The term “photoca-talytic fatigue” denotes a special case of the photo-degradation of polymers resulted only in a change in the strength value of the material. We review not numerous published data on investigations of changes in mechanical properties of polymeric nanocomposite, and mainly in the strength value, arisen from solar range light irradiation. We compare the degradation processes of polymeric nanocomposites containing photoactive components and of the high-cycle fatigue in metals. Likewise, we propose the use of equations of metal high-cycle fatigue curves as a possible approach to mathematical modeling of the processes of polymeric nanocomposites photodegradation. In this, the number of cycles is substitution with exposure time. Especially, the high-cycle fatigue curve equation for the samples with stress concentrations is considered. The experimental parameters of the “photocatalytic fatigue” equation for polymer nanocomposites containing photoactive components are calculated using the Monte Carlo method.
{"title":"Photocatalytic fatigue of the polymer nanocomposites","authors":"A. V. Orekhov, Yurii M. Artem’ev, G. Pavilaynen","doi":"10.21638/11701/spbu10.2022.308","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.308","url":null,"abstract":"We discuss the change in mechanical properties of polymeric nanocomposites with photoactive components caused by solar range lighting. Given degradation photoassisted processes are related with the semiconductor nature of component photoactive particles as photocatalysts. Semiconductor particles can be transferred into electron-exited states due to light quanta absorption. One possible way out from these states is through redox electrochemical reactions with neighbor molecules. The redox reactions can produce transformations of polymer structure and composition, decreasing its mechanical strength. The term “photoca-talytic fatigue” denotes a special case of the photo-degradation of polymers resulted only in a change in the strength value of the material. We review not numerous published data on investigations of changes in mechanical properties of polymeric nanocomposite, and mainly in the strength value, arisen from solar range light irradiation. We compare the degradation processes of polymeric nanocomposites containing photoactive components and of the high-cycle fatigue in metals. Likewise, we propose the use of equations of metal high-cycle fatigue curves as a possible approach to mathematical modeling of the processes of polymeric nanocomposites photodegradation. In this, the number of cycles is substitution with exposure time. Especially, the high-cycle fatigue curve equation for the samples with stress concentrations is considered. The experimental parameters of the “photocatalytic fatigue” equation for polymer nanocomposites containing photoactive components are calculated using the Monte Carlo method.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"13 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87599505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.310
V. Barseghyan
We consider the problem of optimal boundary control for the equation of string vibrations with given initial, final conditions and given values of the string deflection function at intermediate moments of time and with a quality criterion specified over the entire time interval. Using the method of separation of variables and methods of optimal control theory with multipoint intermediate conditions, optimal boundary controls are constructed for arbitrary numbers of the first harmonics. As an application of the proposed constructive approach, a boundary optimal control is built with a given string deflection function at an intermediate moment of time.
{"title":"Optimal boundary control of string oscillations by displacement at two ends with specified values of deflection function at intermediate moments of time","authors":"V. Barseghyan","doi":"10.21638/11701/spbu10.2022.310","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.310","url":null,"abstract":"We consider the problem of optimal boundary control for the equation of string vibrations with given initial, final conditions and given values of the string deflection function at intermediate moments of time and with a quality criterion specified over the entire time interval. Using the method of separation of variables and methods of optimal control theory with multipoint intermediate conditions, optimal boundary controls are constructed for arbitrary numbers of the first harmonics. As an application of the proposed constructive approach, a boundary optimal control is built with a given string deflection function at an intermediate moment of time.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82796673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.309
V. Tregubov, N. K. Egorova
A detailed analysis of previous works on modeling the left ventricle (LV) of the human heart, starting with mechanical models in the form of the simplest three-dimensional figures (cylinder, sphere, ellipsoid of rotation) and ending with models using real contours of the human heart obtained by ultrasound examination of the human heart. A way of constructing a mechanical LV model based on the processing of its dynamic images obtained using computer and magnetic resonance imaging was proposed. Digitization of these images was carried out using numerical methods developed to create a finite element model were implemented in the CMISS system, which allows the use of finite element analysis methods to solve various complex problems. To avoid the need to operate with huge arrays of numbers (up to 10 thousand numerical values at each time of the MRI study) characteristic points of the three-dimensional LV image were selected and spline interpolation of the model framework written in C++ using the Cmgui module was performed. To describe the work of the mechanical model of LV reduction, the main components of this process were identified: transverse compression, longitudinal contraction and twisting. To describe them, simple mathematical characteristics were used.
{"title":"Construction of a mechanical model of the human heart left ventricle in the process of its contraction","authors":"V. Tregubov, N. K. Egorova","doi":"10.21638/11701/spbu10.2022.309","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.309","url":null,"abstract":"A detailed analysis of previous works on modeling the left ventricle (LV) of the human heart, starting with mechanical models in the form of the simplest three-dimensional figures (cylinder, sphere, ellipsoid of rotation) and ending with models using real contours of the human heart obtained by ultrasound examination of the human heart. A way of constructing a mechanical LV model based on the processing of its dynamic images obtained using computer and magnetic resonance imaging was proposed. Digitization of these images was carried out using numerical methods developed to create a finite element model were implemented in the CMISS system, which allows the use of finite element analysis methods to solve various complex problems. To avoid the need to operate with huge arrays of numbers (up to 10 thousand numerical values at each time of the MRI study) characteristic points of the three-dimensional LV image were selected and spline interpolation of the model framework written in C++ using the Cmgui module was performed. To describe the work of the mechanical model of LV reduction, the main components of this process were identified: transverse compression, longitudinal contraction and twisting. To describe them, simple mathematical characteristics were used.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"129 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79418598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.114
A. Aleksandrov, Al’bert I. Arakelov
This article explores a discrete-time multiagent system on a line. This requires the design of a control protocol providing equidistant agent deployment on a given segment of the line under the constraint that each agent receives information about distances to its neighbors via an auxiliary agent. An approach to the solution of the stated problem is developed. This proves that, under the proposed control protocol, neither communication delay nor switching of communication graph destroy convergence of agents to the equidistant distribution. The results of a numerical simulation confirming the obtained theoretical conclusions are presented.
{"title":"A problem of the equidistant deployment for discrete-time multiagent systems","authors":"A. Aleksandrov, Al’bert I. Arakelov","doi":"10.21638/11701/spbu10.2022.114","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.114","url":null,"abstract":"This article explores a discrete-time multiagent system on a line. This requires the design of a control protocol providing equidistant agent deployment on a given segment of the line under the constraint that each agent receives information about distances to its neighbors via an auxiliary agent. An approach to the solution of the stated problem is developed. This proves that, under the proposed control protocol, neither communication delay nor switching of communication graph destroy convergence of agents to the equidistant distribution. The results of a numerical simulation confirming the obtained theoretical conclusions are presented.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"27 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80997046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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