Pub Date : 2023-06-02DOI: 10.21638/11702/spbu10.2019.110
I. Ashanin, Yulia D. Kluchevskaia, A. A. Makhoro, Valeria Yu. Mechanikova, O. A. Mosolova, S. Polozov, A. Pronikov, V. Rashchikov
At present, a fourth-generation synchrotron radiation source USSR (Synchrotron & Laser), which will the one of the world’s largest scientific centers is being designed in Russia. Its creation will make it possible to carry out experiments to study the structures of a wide range of objects in various disciplines at a qualitatively new level compared to the previous generation of sources. The overall facility layout includes a 6 GeV main storage ring and a linear electron accelerator (linac) at full energy. It is proposed to use one linear accelerator with two RF guns. A RF gun with a photocathode can be used to generate a bunch train for a Free Electron Laser (FEL), a RF gun with a thermionic cathode can be used for injection into a storage ring. Both injectors will operate with the same regular part of the linear accelerator, consisting of 100-120 identical sections. The purposed transverse emittance in the main storage ring will be 50–100 pm.rad. The development of a general linear accelerator scheme in order to minimize the beam energy spread and the output transverse emittance, the optimization of the geometric and electrodynamics parameters of the accelerating structures, and the beam dynamics analysis in this linear accelerator will be discussed in the article. The beam dynamics simulation was performed using the BEAMDULAC code developed at the Department of Electrophysical Facilities of the National Research Nuclear University MEPhI.
{"title":"Beam dynamics simulation in the linear accelerator used as an injector for the 4th generation Specialized Synchrotron Radiation Source SSRS-4","authors":"I. Ashanin, Yulia D. Kluchevskaia, A. A. Makhoro, Valeria Yu. Mechanikova, O. A. Mosolova, S. Polozov, A. Pronikov, V. Rashchikov","doi":"10.21638/11702/spbu10.2019.110","DOIUrl":"https://doi.org/10.21638/11702/spbu10.2019.110","url":null,"abstract":"At present, a fourth-generation synchrotron radiation source USSR (Synchrotron & Laser), which will the one of\u0000the world’s largest scientific centers is being designed in Russia. Its creation will make it possible to carry out\u0000experiments to study the structures of a wide range of objects in various disciplines at a qualitatively new level\u0000compared to the previous generation of sources. The overall facility layout includes a 6 GeV main storage ring\u0000and a linear electron accelerator (linac) at full energy. It is proposed to use one linear accelerator with two RF\u0000guns. A RF gun with a photocathode can be used to generate a bunch train for a Free Electron Laser (FEL), a\u0000RF gun with a thermionic cathode can be used for injection into a storage ring. Both injectors will operate with\u0000the same regular part of the linear accelerator, consisting of 100-120 identical sections. The purposed transverse\u0000emittance in the main storage ring will be 50–100 pm.rad. The development of a general linear accelerator\u0000scheme in order to minimize the beam energy spread and the output transverse emittance, the optimization of\u0000the geometric and electrodynamics parameters of the accelerating structures, and the beam dynamics analysis in\u0000this linear accelerator will be discussed in the article. The beam dynamics simulation was performed using the\u0000BEAMDULAC code developed at the Department of Electrophysical Facilities of the National Research Nuclear\u0000University MEPhI.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76982277","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 : 2023-01-01DOI: 10.21638/11701/spbu10.2023.210
Andrey V. Orekhov, Aleksey Orekhov
Distributed denial-of-service attacks (DDoS attacks) are intrusions into computing systems of the Internet. Their purpose is to make systems of the Internet inaccessible for users. DDoS attack consist of sending many requests to a certain resource at the same time. As a result, the server cannot withstand the network load. In such situation, a provider must determine the moment when attack begins and change the traffic management strategy. Detection of the beginning of a DDoS attack is possible by using unsupervised machine learning methods and sequential statistical analysis of network activity. To activate that, convenient to use mathematical models based on discrete random processes with monotonically increasing trajectories. Random functions, which are represented in the correspondence between generalized time and the cumulative sum of network traffic or the correspondence between the total number of incoming packets and the cumulative sum of packets processed, change their type of increasing from linear to non-linear. In the first case, to parabolic or exponential, in the second case to logarithmic or arctangent. To determine the moment when the type of increasing is going to change, one can use quadratic forms of approximation-estimation tests as statistical rules.
{"title":"Network traffic anomalies automatic detection in DDoS attacks","authors":"Andrey V. Orekhov, Aleksey Orekhov","doi":"10.21638/11701/spbu10.2023.210","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.210","url":null,"abstract":"Distributed denial-of-service attacks (DDoS attacks) are intrusions into computing systems of the Internet. Their purpose is to make systems of the Internet inaccessible for users. DDoS attack consist of sending many requests to a certain resource at the same time. As a result, the server cannot withstand the network load. In such situation, a provider must determine the moment when attack begins and change the traffic management strategy. Detection of the beginning of a DDoS attack is possible by using unsupervised machine learning methods and sequential statistical analysis of network activity. To activate that, convenient to use mathematical models based on discrete random processes with monotonically increasing trajectories. Random functions, which are represented in the correspondence between generalized time and the cumulative sum of network traffic or the correspondence between the total number of incoming packets and the cumulative sum of packets processed, change their type of increasing from linear to non-linear. In the first case, to parabolic or exponential, in the second case to logarithmic or arctangent. To determine the moment when the type of increasing is going to change, one can use quadratic forms of approximation-estimation tests as statistical rules.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81340072","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 : 2023-01-01DOI: 10.21638/11701/spbu10.2023.104
Rustam Saakyan, I. Shpekht, Gevorg A. Petrosyan
The study aims to develop optimal approaches to the search for borrowings in scientific works. The article discusses the stages of searching for the presence of borrowings, such as preprocessing, rough filtering of texts, searching for similar texts, and searching for borrowings. The main focus is on the description of approaches and techniques that can be effectively implemented at each stage. For example, for the preprocessing stage, it may be converting text characters from uppercase to lowercase, removing punctuation marks, and removing stop words. For the stage of rough text filtering, it is filters by topic and word frequency. It may be calculating the importance of words in the context of the text and representing the word as a vector in multidimensional space to determine the proximity measure for the stage of finding similar texts. Finally, it is a search for an exact match, paraphrases and a measure of similarity of expressions for the stage of finding borrowings. The scientific novelty lies in using Markov chains to find the similarity of texts for the second and third stages of the search for borrowings proposed by authors. As a result, the example shows the technique of using Markov chains for text representation, searching for the most frequently occurring words, building a graph of a Markov chain of words, and the prospects for using Markov chains of texts for rough filtering and searching for similar texts.
{"title":"Finding the presence of borrowings in scientific works based on Markov chains","authors":"Rustam Saakyan, I. Shpekht, Gevorg A. Petrosyan","doi":"10.21638/11701/spbu10.2023.104","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.104","url":null,"abstract":"The study aims to develop optimal approaches to the search for borrowings in scientific works. The article discusses the stages of searching for the presence of borrowings, such as preprocessing, rough filtering of texts, searching for similar texts, and searching for borrowings. The main focus is on the description of approaches and techniques that can be effectively implemented at each stage. For example, for the preprocessing stage, it may be converting text characters from uppercase to lowercase, removing punctuation marks, and removing stop words. For the stage of rough text filtering, it is filters by topic and word frequency. It may be calculating the importance of words in the context of the text and representing the word as a vector in multidimensional space to determine the proximity measure for the stage of finding similar texts. Finally, it is a search for an exact match, paraphrases and a measure of similarity of expressions for the stage of finding borrowings. The scientific novelty lies in using Markov chains to find the similarity of texts for the second and third stages of the search for borrowings proposed by authors. As a result, the example shows the technique of using Markov chains for text representation, searching for the most frequently occurring words, building a graph of a Markov chain of words, and the prospects for using Markov chains of texts for rough filtering and searching for similar texts.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80732807","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 : 2023-01-01DOI: 10.21638/11701/spbu10.2023.203
Nataliya A. Zhabko, V. Karelin, V. Provotorov, S. Sergeev
The article considers the Navier — Stokes evolutionary differential system used in the mathematical description of the evolutionary processes of transportation of various types of liquids through network or main pipelines. The Navier—Stokes system is considered in Sobolev spaces, the elements of which are functions with carriers on n-dimensional networklike domains. These domains are a totality of a finite number of mutually non-intersecting subdomains connected to each other by parts of the surfaces of their boundaries like a graph (in applications these are the places of branching of pipelines). Two main questions of analysis are discussed: the weak solvability of the initial boundary value problem of the Navier — Stokes system and the optimal control of this system. The main method of research of weak solutions is the semidigitization of the input system by a time variable, that is the reduction of a differential system to a differential-difference system, and using a priori estimates for weak solutions of boundary value problems to prove the theorem of the existence of a solution of the input differential system. For the optimal control problem a minimizing functional (the penalty function) and a family of the approximate functional with parameters that characterize the “penalty” for failure to fulfill the equations of state of the system are introduced. At the same time, a special Hilbert space is created, the elements of which are pairs of functions that describe the state of the system and controlling actions. The convergence of the sequence of such functions to the optimal state of the system and its corresponding optimal control is proved. The latter essentially widen the possibilities of analysis of stationary and nonstationary network-like processes of hydrodynamics and optimal control of these processesd.
{"title":"The method of penalty functions in the analysis of optimal control problems of Navier — Stokes evolutionary systems with a spatial variable in a network-like domain","authors":"Nataliya A. Zhabko, V. Karelin, V. Provotorov, S. Sergeev","doi":"10.21638/11701/spbu10.2023.203","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.203","url":null,"abstract":"The article considers the Navier — Stokes evolutionary differential system used in the mathematical description of the evolutionary processes of transportation of various types of liquids through network or main pipelines. The Navier—Stokes system is considered in Sobolev spaces, the elements of which are functions with carriers on n-dimensional networklike domains. These domains are a totality of a finite number of mutually non-intersecting subdomains connected to each other by parts of the surfaces of their boundaries like a graph (in applications these are the places of branching of pipelines). Two main questions of analysis are discussed: the weak solvability of the initial boundary value problem of the Navier — Stokes system and the optimal control of this system. The main method of research of weak solutions is the semidigitization of the input system by a time variable, that is the reduction of a differential system to a differential-difference system, and using a priori estimates for weak solutions of boundary value problems to prove the theorem of the existence of a solution of the input differential system. For the optimal control problem a minimizing functional (the penalty function) and a family of the approximate functional with parameters that characterize the “penalty” for failure to fulfill the equations of state of the system are introduced. At the same time, a special Hilbert space is created, the elements of which are pairs of functions that describe the state of the system and controlling actions. The convergence of the sequence of such functions to the optimal state of the system and its corresponding optimal control is proved. The latter essentially widen the possibilities of analysis of stationary and nonstationary network-like processes of hydrodynamics and optimal control of these processesd.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84808114","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 : 2023-01-01DOI: 10.21638/11701/spbu10.2023.201
M. Abbasov, A. S. Sharlay
The paper studies a method for finding the cost-optimal trajectory of a road connecting two points on a given terrain. Situations are considered when the cost of delivery of materials is a constant value, as well as a more general formulation of the problem, in which the cost of delivery depends on the coordinate of a point. In each case, an integral functional is constructed cost, the argument in which is a function that describes the trajectory of the path. The Ritz method is used to find an approximate solution. It is set analytically, in the form of a trigonometric polynomial, which increases the convenience of processing and further research of the results obtained in comparison with the numerical solution of the necessary conditions for the extremum of the investigated functional. The paper also discusses the problem of convergence. Illustrative examples are given.
{"title":"Method for finding the cost-optimal road trajectory on the surface of the terrain","authors":"M. Abbasov, A. S. Sharlay","doi":"10.21638/11701/spbu10.2023.201","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.201","url":null,"abstract":"The paper studies a method for finding the cost-optimal trajectory of a road connecting two points on a given terrain. Situations are considered when the cost of delivery of materials is a constant value, as well as a more general formulation of the problem, in which the cost of delivery depends on the coordinate of a point. In each case, an integral functional is constructed cost, the argument in which is a function that describes the trajectory of the path. The Ritz method is used to find an approximate solution. It is set analytically, in the form of a trigonometric polynomial, which increases the convenience of processing and further research of the results obtained in comparison with the numerical solution of the necessary conditions for the extremum of the investigated functional. The paper also discusses the problem of convergence. Illustrative examples are given.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81930658","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 : 2023-01-01DOI: 10.21638/11701/spbu10.2023.106
N. V. Egorov, E. Vinogradova, G. Doronin
In this paper the results of a two-dimensional diode emission system based on a blade-like field cathode in a polar coordinate system modeling is presented. The top of the emitter is a circle with a dielectric coating. The anode is a circle coaxial to the top of the emitter. The boundary condition of the first kind is set on the cathode, and the first and second kind on the anode. The problem of calculating the electrostatic potential distribution is reduced to solving a system of linear algebraic equations with constant coefficients. All the geometric dimensions of the system and the values of the potentials on the electrodes are the parameters of the problem.
{"title":"Blade-like field cathode with a dielectric coating mathematical modeling","authors":"N. V. Egorov, E. Vinogradova, G. Doronin","doi":"10.21638/11701/spbu10.2023.106","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.106","url":null,"abstract":"In this paper the results of a two-dimensional diode emission system based on a blade-like field cathode in a polar coordinate system modeling is presented. The top of the emitter is a circle with a dielectric coating. The anode is a circle coaxial to the top of the emitter. The boundary condition of the first kind is set on the cathode, and the first and second kind on the anode. The problem of calculating the electrostatic potential distribution is reduced to solving a system of linear algebraic equations with constant coefficients. All the geometric dimensions of the system and the values of the potentials on the electrodes are the parameters of the problem.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79651911","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 : 2023-01-01DOI: 10.21638/11701/spbu10.2023.212
O. Baskov, D. Potapov
We consider the Sturm — Liouville problem with discontinuous nonlinearity, control and perturbation. Previously obtained results for equations with a spectral parameter and a discontinuous operator are applied to this problem. By the variational method, we have established theorems on the existence of solutions to the Sturm — Liouville problem with discontinuous nonlinearity and to the optimal control problem, as well as on topological properties of the set of the acceptable “control — state” pairs. A one-dimensional analog of the Gol’dshtik model for separated flows of an incompressible fluid with control and perturbation is given as an application.
{"title":"Control and perturbation in Sturm — Liouville’s problem with discontinuous nonlinearity","authors":"O. Baskov, D. Potapov","doi":"10.21638/11701/spbu10.2023.212","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.212","url":null,"abstract":"We consider the Sturm — Liouville problem with discontinuous nonlinearity, control and perturbation. Previously obtained results for equations with a spectral parameter and a discontinuous operator are applied to this problem. By the variational method, we have established theorems on the existence of solutions to the Sturm — Liouville problem with discontinuous nonlinearity and to the optimal control problem, as well as on topological properties of the set of the acceptable “control — state” pairs. A one-dimensional analog of the Gol’dshtik model for separated flows of an incompressible fluid with control and perturbation is given as an application.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91271166","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 : 2023-01-01DOI: 10.21638/11701/spbu10.2023.202
A. Egorov
The paper gives sufficient conditions for the solvability of the generalized Myshkis problem for a system of equations with a distributed time-varying delay and a constant kernel. Conditions on the kernel which guarantee the uniform stability of the system for any admissible delay are obtained. The admissible delay in this paper is a piecewise continuous function bounded from above in magnitude and growth rate. The applicability of the obtained conditions is illustrated by two examples.
{"title":"Razumikhin approach in the generalized Myshkis problem for systems with distributed delay","authors":"A. Egorov","doi":"10.21638/11701/spbu10.2023.202","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.202","url":null,"abstract":"The paper gives sufficient conditions for the solvability of the generalized Myshkis problem for a system of equations with a distributed time-varying delay and a constant kernel. Conditions on the kernel which guarantee the uniform stability of the system for any admissible delay are obtained. The admissible delay in this paper is a piecewise continuous function bounded from above in magnitude and growth rate. The applicability of the obtained conditions is illustrated by two examples.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82070767","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 : 2023-01-01DOI: 10.21638/11701/spbu10.2023.109
S. Zavadskiy, Dmitrii A. Ovsyannikov, Dmitrii D. Melnikov
The optimization approach is applied to the synthesis and optimization of nonlinear real-time feedback optimal control system of a certain Maglev platform. To optimize the nonlinear control law, the integral functional criteria is minimized, which evaluates the quality of the dynamics of not one trajectory, but an ensemble of nonlinear trajectories of the system. The considered ensemble of trajectories covers the entire area of the engineering gap between the platform and the guide rails. In this area the magnetic forces provide highly nonlinear effects due to the considered design features of the object. At the same time, it is required to provide the stabilization within the entire engineering gap. It makes this statement to be a multi-input nonlinear control problem. The components of the feedback control law vector have a polynomial form of the state-space variables. As a result of computational optimization of trajectories ensemble, a class of Pareto-optimal polynomial regulators is constructed for considered control object. In the presented set, each Pareto-optimal point corresponds to a specific designed controller and investigated functional criteria which evaluates the entire ensemble of perturbed nonlinear trajectories. This allows a research engineer to choose various nonlinear regulators and achieve a compromise between stabilization accuracy and energy costs.
{"title":"Optimization approach to the design of nonlinear control system controllers","authors":"S. Zavadskiy, Dmitrii A. Ovsyannikov, Dmitrii D. Melnikov","doi":"10.21638/11701/spbu10.2023.109","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.109","url":null,"abstract":"The optimization approach is applied to the synthesis and optimization of nonlinear real-time feedback optimal control system of a certain Maglev platform. To optimize the nonlinear control law, the integral functional criteria is minimized, which evaluates the quality of the dynamics of not one trajectory, but an ensemble of nonlinear trajectories of the system. The considered ensemble of trajectories covers the entire area of the engineering gap between the platform and the guide rails. In this area the magnetic forces provide highly nonlinear effects due to the considered design features of the object. At the same time, it is required to provide the stabilization within the entire engineering gap. It makes this statement to be a multi-input nonlinear control problem. The components of the feedback control law vector have a polynomial form of the state-space variables. As a result of computational optimization of trajectories ensemble, a class of Pareto-optimal polynomial regulators is constructed for considered control object. In the presented set, each Pareto-optimal point corresponds to a specific designed controller and investigated functional criteria which evaluates the entire ensemble of perturbed nonlinear trajectories. This allows a research engineer to choose various nonlinear regulators and achieve a compromise between stabilization accuracy and energy costs.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76891728","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 : 2023-01-01DOI: 10.21638/11701/spbu10.2023.206
D. Qi, V. Bure
The continued economic development of various countries or regions has resulted in increased competition in global markets, leading to a concentration of investors and skilled labour in locations with high investment attractiveness. The investment attractiveness of a given country or region is determined by its investment potential and risk, which are characterized by a combination of various significant factors.This paper seeks to develop an econometric model to estimate the amount of investment in fixed capital in a specific region, taking into consideration the linear relationship between the observed results, in order to determine the main conditions that are necessary for achieving stable and high economic growth. These conditions include the acceleration of investment activity and the implementation of major national reforms to ensure the effectiveness of the investment process. To assess the overall influence of the financial and economic indicators studied on the volume of investment, multiple regression analysis was utilized as the primary mathematical tool of the study. Furthermore, assumptions were made regarding the rank of the observations. To validate this hypothesis, a cluster analysis was conducted, grouping the observations into four clusters based on their results, depending on the volume of investment or the geographical characteristics of the region.
{"title":"Research of investment attractiveness based on cluster analysis","authors":"D. Qi, V. Bure","doi":"10.21638/11701/spbu10.2023.206","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.206","url":null,"abstract":"The continued economic development of various countries or regions has resulted in increased competition in global markets, leading to a concentration of investors and skilled labour in locations with high investment attractiveness. The investment attractiveness of a given country or region is determined by its investment potential and risk, which are characterized by a combination of various significant factors.This paper seeks to develop an econometric model to estimate the amount of investment in fixed capital in a specific region, taking into consideration the linear relationship between the observed results, in order to determine the main conditions that are necessary for achieving stable and high economic growth. These conditions include the acceleration of investment activity and the implementation of major national reforms to ensure the effectiveness of the investment process. To assess the overall influence of the financial and economic indicators studied on the volume of investment, multiple regression analysis was utilized as the primary mathematical tool of the study. Furthermore, assumptions were made regarding the rank of the observations. To validate this hypothesis, a cluster analysis was conducted, grouping the observations into four clusters based on their results, depending on the volume of investment or the geographical characteristics of the region.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86132852","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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