Pub Date : 2015-12-03DOI: 10.1109/SCP.2015.7342154
V. Maximov, I. Nudner
Analytical solution of a problem of surface waves interaction with M fixed rectangular obstacles in a fluid of finite depth is constructed. The fluid is supposed to be ideal, incompressible, homogeneous, and its motion has a velocity potential. Small oscillations of the fluid caused by interaction of incoming waves and obstacles are considered. A linear two-dimensional mixed problem for the Laplace equation is solved by the partition method in subareas and by the linear operator expansion in terms of eigenfunctions. Orthogonalization procedure is applied to simplify the system of infinite linear algebraic equations. The system solutions produce the terms of the generalised Fourier series for the velocity potential of the fluid motion. All necessary kinematic and dynamic wave characteristics of movement and force interaction between waves and obstacles are calculated. Possibility of the received solution application to obstacles with more complicated shapes is demonstrated.
{"title":"Surface waves interaction with the system of M fixed rectangular obstacles in the fluid of finite depth","authors":"V. Maximov, I. Nudner","doi":"10.1109/SCP.2015.7342154","DOIUrl":"https://doi.org/10.1109/SCP.2015.7342154","url":null,"abstract":"Analytical solution of a problem of surface waves interaction with M fixed rectangular obstacles in a fluid of finite depth is constructed. The fluid is supposed to be ideal, incompressible, homogeneous, and its motion has a velocity potential. Small oscillations of the fluid caused by interaction of incoming waves and obstacles are considered. A linear two-dimensional mixed problem for the Laplace equation is solved by the partition method in subareas and by the linear operator expansion in terms of eigenfunctions. Orthogonalization procedure is applied to simplify the system of infinite linear algebraic equations. The system solutions produce the terms of the generalised Fourier series for the velocity potential of the fluid motion. All necessary kinematic and dynamic wave characteristics of movement and force interaction between waves and obstacles are calculated. Possibility of the received solution application to obstacles with more complicated shapes is demonstrated.","PeriodicalId":110366,"journal":{"name":"2015 International Conference \"Stability and Control Processes\" in Memory of V.I. Zubov (SCP)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114772177","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 : 2015-12-03DOI: 10.1109/SCP.2015.7342140
L. Vladimirova, I. Fatyanova
In this paper, we consider the classical linear regression of the second order, the unknown parameters are usually evaluated by the method of least squares. The distribution of the error of parameter vector estimate depends on the plan choice. This choice is carried out to minimize the generalized variance of unknown parameters estimate or to maximize the information matrix determinant. To solve this extremal problem the random search is used on the basis of on the normal distribution. This method takes into account the information on the objective function by the use of covariance matrix. This method is iterative; at each iteration the search domain is gradually contracted round the point recognized to be most promising at previous iteration. So we have self-training method (named the method with a “memory”). The algorithm is simple and can be used for large dimension of search domain. In addition, this method is suitable for parallelization by distributing of numerical statistical tests among the processes [1, 2].
{"title":"Construction of regression experiment optimal plan using parallel computing","authors":"L. Vladimirova, I. Fatyanova","doi":"10.1109/SCP.2015.7342140","DOIUrl":"https://doi.org/10.1109/SCP.2015.7342140","url":null,"abstract":"In this paper, we consider the classical linear regression of the second order, the unknown parameters are usually evaluated by the method of least squares. The distribution of the error of parameter vector estimate depends on the plan choice. This choice is carried out to minimize the generalized variance of unknown parameters estimate or to maximize the information matrix determinant. To solve this extremal problem the random search is used on the basis of on the normal distribution. This method takes into account the information on the objective function by the use of covariance matrix. This method is iterative; at each iteration the search domain is gradually contracted round the point recognized to be most promising at previous iteration. So we have self-training method (named the method with a “memory”). The algorithm is simple and can be used for large dimension of search domain. In addition, this method is suitable for parallelization by distributing of numerical statistical tests among the processes [1, 2].","PeriodicalId":110366,"journal":{"name":"2015 International Conference \"Stability and Control Processes\" in Memory of V.I. Zubov (SCP)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115139381","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 : 2015-12-03DOI: 10.1109/SCP.2015.7342067
V. Provotorov
The optimal boundary control problem for a differential system with delay and distributed parameters on the graph is considered. The spaces of integrable functions are used as state-space systems and the space of boundary control and observation. The conditions of the unique solvability of the problem of optimal control are obtained.
{"title":"Boundary control of a parabolic system with delay and distributed parameters on the graph","authors":"V. Provotorov","doi":"10.1109/SCP.2015.7342067","DOIUrl":"https://doi.org/10.1109/SCP.2015.7342067","url":null,"abstract":"The optimal boundary control problem for a differential system with delay and distributed parameters on the graph is considered. The spaces of integrable functions are used as state-space systems and the space of boundary control and observation. The conditions of the unique solvability of the problem of optimal control are obtained.","PeriodicalId":110366,"journal":{"name":"2015 International Conference \"Stability and Control Processes\" in Memory of V.I. Zubov (SCP)","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115466703","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 : 2015-12-03DOI: 10.1109/SCP.2015.7342135
A. Shmyrov, V. Shmyrov
In this paper we consider controllable orbital motion in a neighborhood of the first collinear libration point L1 of the Sun-Earth system. This libration point is unstable. For a long stay of the spacecraft in this area of space required the control action. We model the motion by equations circular restricted three-body problem. At the same time, we use non-linear approximation of these equations, so-called Hills equations and linearized equations. For solution of the problem of stabilization of motion, we use the model of linear-quadratic optimization. This model offers a standard approach for the construction of stabilizing control laws. In this work, we present an original family of quadratic functionals, which were built with the help of the special linear function of the phase variables, so-called “hazard function”. The increase of module of this function module mean departure of a spacecraft from a neighborhood of the libration point and the decrease of this module corresponds to the stabilization of motion. For the represented family of functionals we have built the Bellman function and showed that the control damps square of hazard function. Numerical simulations of the orbital motion with obtained controls is realized in the nonlinear model of Hills equations and in model of circular three-body problem.
{"title":"The criteria of quality in the problem of motion stabilization in a neighborhood of collinear libration point","authors":"A. Shmyrov, V. Shmyrov","doi":"10.1109/SCP.2015.7342135","DOIUrl":"https://doi.org/10.1109/SCP.2015.7342135","url":null,"abstract":"In this paper we consider controllable orbital motion in a neighborhood of the first collinear libration point L1 of the Sun-Earth system. This libration point is unstable. For a long stay of the spacecraft in this area of space required the control action. We model the motion by equations circular restricted three-body problem. At the same time, we use non-linear approximation of these equations, so-called Hills equations and linearized equations. For solution of the problem of stabilization of motion, we use the model of linear-quadratic optimization. This model offers a standard approach for the construction of stabilizing control laws. In this work, we present an original family of quadratic functionals, which were built with the help of the special linear function of the phase variables, so-called “hazard function”. The increase of module of this function module mean departure of a spacecraft from a neighborhood of the libration point and the decrease of this module corresponds to the stabilization of motion. For the represented family of functionals we have built the Bellman function and showed that the control damps square of hazard function. Numerical simulations of the orbital motion with obtained controls is realized in the nonlinear model of Hills equations and in model of circular three-body problem.","PeriodicalId":110366,"journal":{"name":"2015 International Conference \"Stability and Control Processes\" in Memory of V.I. Zubov (SCP)","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123570338","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 : 2015-12-03DOI: 10.1109/SCP.2015.7342069
A. Tikhonov
A satellite with electrodynamic attitude control system is considered. The problem of compensation of an external disturbing torque is solved. The optimization of control process in vicinity of programmed motion is achieved on the basis of control system without involving additional measuring devices.
{"title":"On electrodynamical compensation of a torque disturbing satellite orientation","authors":"A. Tikhonov","doi":"10.1109/SCP.2015.7342069","DOIUrl":"https://doi.org/10.1109/SCP.2015.7342069","url":null,"abstract":"A satellite with electrodynamic attitude control system is considered. The problem of compensation of an external disturbing torque is solved. The optimization of control process in vicinity of programmed motion is achieved on the basis of control system without involving additional measuring devices.","PeriodicalId":110366,"journal":{"name":"2015 International Conference \"Stability and Control Processes\" in Memory of V.I. Zubov (SCP)","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122718009","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 : 2015-12-03DOI: 10.1109/SCP.2015.7342039
G. Ivanov, A. Sharlay
This paper is devoted to necessary and sufficient conditions of stability of linear switched systems. To establish a stability criterion for the considered class of linear systems the set-theoretic approach is proposed to be used.
{"title":"On stability of linear homogeneous switched systems","authors":"G. Ivanov, A. Sharlay","doi":"10.1109/SCP.2015.7342039","DOIUrl":"https://doi.org/10.1109/SCP.2015.7342039","url":null,"abstract":"This paper is devoted to necessary and sufficient conditions of stability of linear switched systems. To establish a stability criterion for the considered class of linear systems the set-theoretic approach is proposed to be used.","PeriodicalId":110366,"journal":{"name":"2015 International Conference \"Stability and Control Processes\" in Memory of V.I. Zubov (SCP)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125149843","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 : 2015-12-03DOI: 10.1109/SCP.2015.7342060
E. Polyakhova, V. Starkov, N. Stepenko
Solar sailing is an unique form of spacecraft propulsion that uses the free and limitless supply of photons from the Sun. The investigation of near-the-Sun space properties is of the great scientific interest. It can be realized by the help of solar sailing. We present the numerical simulation of several closed modelled trajectories of a spacecraft with a controlled solar sail to reach heliopolar regions, to fly over the Sun north and south poles and to return to the Earth orbit.
{"title":"Solar sailing out of ecliptic plane","authors":"E. Polyakhova, V. Starkov, N. Stepenko","doi":"10.1109/SCP.2015.7342060","DOIUrl":"https://doi.org/10.1109/SCP.2015.7342060","url":null,"abstract":"Solar sailing is an unique form of spacecraft propulsion that uses the free and limitless supply of photons from the Sun. The investigation of near-the-Sun space properties is of the great scientific interest. It can be realized by the help of solar sailing. We present the numerical simulation of several closed modelled trajectories of a spacecraft with a controlled solar sail to reach heliopolar regions, to fly over the Sun north and south poles and to return to the Earth orbit.","PeriodicalId":110366,"journal":{"name":"2015 International Conference \"Stability and Control Processes\" in Memory of V.I. Zubov (SCP)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126209136","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 : 2015-12-03DOI: 10.1109/SCP.2015.7342098
G. M. Vorobev, M. Ignatev, T. S. Katermina
The problem of retention of the plasma column in a tokamak-type systems is key in the development of fusion energy [1, 4]. Based on the method of redundant variables synthesized ultrastability oscillator model that can be used to hold the plasma column.
{"title":"Retention of plasma column in tokamak","authors":"G. M. Vorobev, M. Ignatev, T. S. Katermina","doi":"10.1109/SCP.2015.7342098","DOIUrl":"https://doi.org/10.1109/SCP.2015.7342098","url":null,"abstract":"The problem of retention of the plasma column in a tokamak-type systems is key in the development of fusion energy [1, 4]. Based on the method of redundant variables synthesized ultrastability oscillator model that can be used to hold the plasma column.","PeriodicalId":110366,"journal":{"name":"2015 International Conference \"Stability and Control Processes\" in Memory of V.I. Zubov (SCP)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129517700","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 : 2015-12-03DOI: 10.1109/SCP.2015.7342040
V. V. Kolbin, D. Perestoronin
This article focuses on the issue of how to study the stability of solutions to a multi-objective optimization problem. Normalization and principle of choice of solutions to a multi-objective optimization problem can be approached in various ways. The concepts of the region of admissibility and scope of optimality are also given into consideration. We consider the ε-stability in the medium multi-objective optimization problem.
{"title":"Several problems of the stability of multi-objective optimization","authors":"V. V. Kolbin, D. Perestoronin","doi":"10.1109/SCP.2015.7342040","DOIUrl":"https://doi.org/10.1109/SCP.2015.7342040","url":null,"abstract":"This article focuses on the issue of how to study the stability of solutions to a multi-objective optimization problem. Normalization and principle of choice of solutions to a multi-objective optimization problem can be approached in various ways. The concepts of the region of admissibility and scope of optimality are also given into consideration. We consider the ε-stability in the medium multi-objective optimization problem.","PeriodicalId":110366,"journal":{"name":"2015 International Conference \"Stability and Control Processes\" in Memory of V.I. Zubov (SCP)","volume":"2228 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130187435","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 : 2015-12-03DOI: 10.1109/SCP.2015.7342045
Sergey S. Fadeev
A nonlinear mechanical system with nonconservative forces, two-component homogeneous potential forces and control forces of a special form is considered. On the basis of the Lyapunov functions method, several theorems that provide sufficient conditions of asymptotic stability of system's equilibrium position and sufficient conditions of ultimate boundedness of its solutions are proved.
{"title":"On the stability and ultimate boundedness of motions of a class of nonlinear mechanical systems","authors":"Sergey S. Fadeev","doi":"10.1109/SCP.2015.7342045","DOIUrl":"https://doi.org/10.1109/SCP.2015.7342045","url":null,"abstract":"A nonlinear mechanical system with nonconservative forces, two-component homogeneous potential forces and control forces of a special form is considered. On the basis of the Lyapunov functions method, several theorems that provide sufficient conditions of asymptotic stability of system's equilibrium position and sufficient conditions of ultimate boundedness of its solutions are proved.","PeriodicalId":110366,"journal":{"name":"2015 International Conference \"Stability and Control Processes\" in Memory of V.I. Zubov (SCP)","volume":"7 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116816771","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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