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.2015.7342067
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.2015.7342045
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}
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.2015.7342144
G. Bilchenko
The possibility to find close-to-convex functions in a class of unit disk mapping onto bounded polygonal domain with rectilinear boundary by means of Schwartz-Christoffel integrals is investigated in the conditions of all possible exponents permutations. The notions of reducible and irreducible exponents collections and uniformly reducible set of collection are introduced. Linear programming problems series solving is offered for investigation of uniformly reducibility of set. An algorithm optimizing the computations by means of special subset of series construction is elaborated. The search of reducing permutation is replaced by search of special Hamiltonian cycle in complete graph. The sufficient conditions of reducibility and irreducibility are obtained. The examples of irreducible collections are constructed. The methods of constructions of new collections from old ones are given. For the above mentioned class of Schwartz-Christoffel integrals the Paatero's theorem about sufficient condition of univalence is generalized.
{"title":"Schwartz-Christoffel integrals reducibility to close-to-convex","authors":"G. Bilchenko","doi":"10.1109/SCP.2015.7342144","DOIUrl":"https://doi.org/10.1109/SCP.2015.7342144","url":null,"abstract":"The possibility to find close-to-convex functions in a class of unit disk mapping onto bounded polygonal domain with rectilinear boundary by means of Schwartz-Christoffel integrals is investigated in the conditions of all possible exponents permutations. The notions of reducible and irreducible exponents collections and uniformly reducible set of collection are introduced. Linear programming problems series solving is offered for investigation of uniformly reducibility of set. An algorithm optimizing the computations by means of special subset of series construction is elaborated. The search of reducing permutation is replaced by search of special Hamiltonian cycle in complete graph. The sufficient conditions of reducibility and irreducibility are obtained. The examples of irreducible collections are constructed. The methods of constructions of new collections from old ones are given. For the above mentioned class of Schwartz-Christoffel integrals the Paatero's theorem about sufficient condition of univalence is generalized.","PeriodicalId":110366,"journal":{"name":"2015 International Conference \"Stability and Control Processes\" in Memory of V.I. Zubov (SCP)","volume":"109 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":"114560972","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.2015.7342060
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.2015.7342044
A. Aleksandrov, E. Aleksandrova, A. Platonov, G. Dai
A switched system generated by the family of homogeneous subsystems with homogeneity orders less than one is studied. It is assumed that the zero solution of each subsystem is asymptotically stable. On the basis of the dwell-time approach, conditions on switching law are determined under which a given spherical neighborhood of the origin is contained in the attraction domain of the zero solution of the corresponding hybrid system.
{"title":"Stability analysis and estimation of the attraction domain for a class of hybrid nonlinear systems","authors":"A. Aleksandrov, E. Aleksandrova, A. Platonov, G. Dai","doi":"10.1109/SCP.2015.7342044","DOIUrl":"https://doi.org/10.1109/SCP.2015.7342044","url":null,"abstract":"A switched system generated by the family of homogeneous subsystems with homogeneity orders less than one is studied. It is assumed that the zero solution of each subsystem is asymptotically stable. On the basis of the dwell-time approach, conditions on switching law are determined under which a given spherical neighborhood of the origin is contained in the attraction domain of the zero solution of the corresponding hybrid system.","PeriodicalId":110366,"journal":{"name":"2015 International Conference \"Stability and Control Processes\" in Memory of V.I. Zubov (SCP)","volume":"14 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":"114503375","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.2015.7342042
B. Zimin, I. Zorin
The authors consider two different ways to solve the problem of stability of a flat form of equilibrium of plate with a through crack. Methods of estimating of critical loading are in the paper. The possibility of non-straight crack moving is demonstrated.
{"title":"On the problem of stability of a planar equilibrum shape of a thin plate with through cracks","authors":"B. Zimin, I. Zorin","doi":"10.1109/SCP.2015.7342042","DOIUrl":"https://doi.org/10.1109/SCP.2015.7342042","url":null,"abstract":"The authors consider two different ways to solve the problem of stability of a flat form of equilibrium of plate with a through crack. Methods of estimating of critical loading are in the paper. The possibility of non-straight crack moving is demonstrated.","PeriodicalId":110366,"journal":{"name":"2015 International Conference \"Stability and Control Processes\" in Memory of V.I. Zubov (SCP)","volume":"21 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114132469","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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