Pub Date : 2020-06-01DOI: 10.1109/STAB49150.2020.9140473
A. Krishchenko, E. Tverskaya
To study equilibrium points with positive coordinates, we use the localization method and find sets containing all compact invariant sets lying in the region with positive values of the variables. These sets are bounded by level surfaces of coordinate functions. We consider two– and four–dimensional systems and indicate the cases when these sets are defined by two inner equilibrium points.
{"title":"Analysis of systems with non-negative variables using the localization method","authors":"A. Krishchenko, E. Tverskaya","doi":"10.1109/STAB49150.2020.9140473","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140473","url":null,"abstract":"To study equilibrium points with positive coordinates, we use the localization method and find sets containing all compact invariant sets lying in the region with positive values of the variables. These sets are bounded by level surfaces of coordinate functions. We consider two– and four–dimensional systems and indicate the cases when these sets are defined by two inner equilibrium points.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121816116","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 : 2020-06-01DOI: 10.1109/STAB49150.2020.9140564
N. Bolotnik, T. Figurina
For a system of two bodies on an inclined plane with Coulomb’s friction, the in-principle possibility for driving the system to an arbitrary terminal state of rest by means of control of the interaction force between the bodies is proved for the case where the bodies do not rest on the common line of maximum slope in the initial state. A control algorithm that combines quasistatic and fast motions is designed.
{"title":"Control of a system of two interacting bodies on a rough inclined plane","authors":"N. Bolotnik, T. Figurina","doi":"10.1109/STAB49150.2020.9140564","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140564","url":null,"abstract":"For a system of two bodies on an inclined plane with Coulomb’s friction, the in-principle possibility for driving the system to an arbitrary terminal state of rest by means of control of the interaction force between the bodies is proved for the case where the bodies do not rest on the common line of maximum slope in the initial state. A control algorithm that combines quasistatic and fast motions is designed.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130198315","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 : 2020-06-01DOI: 10.1109/STAB49150.2020.9140540
V. Korneev
A problem of protection of an object on a movable base from transient impacts by means of an active shock isolator is considered. The peak magnitude of the displacement of the object relative to the base is chosen as the performance index to be minimized. Based on the optimal control without anticipation for the instantaneous impact, a guaranteeing control with optimized instant of engagement is constructed. The control that involves optimization of the engagement instant is compared with other control strategies.
{"title":"Anticipation and Delay for a Constant-force Control in the Problem of Protection of an Object on a Movable Base from an Impact","authors":"V. Korneev","doi":"10.1109/STAB49150.2020.9140540","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140540","url":null,"abstract":"A problem of protection of an object on a movable base from transient impacts by means of an active shock isolator is considered. The peak magnitude of the displacement of the object relative to the base is chosen as the performance index to be minimized. Based on the optimal control without anticipation for the instantaneous impact, a guaranteeing control with optimized instant of engagement is constructed. The control that involves optimization of the engagement instant is compared with other control strategies.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128826233","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 : 2020-06-01DOI: 10.1109/STAB49150.2020.9140498
Y. Somov, S. Butyrin, S. Somov
The methods for guidance and motion control of a space robot are presented when the visual inspecting the technical state of a geostationary information satellite.
介绍了在对地静止信息卫星技术状态进行目视检测时，空间机器人的制导和运动控制方法。
{"title":"Motion Control of Space Robot at an Inspection of Geostationary Satellite State","authors":"Y. Somov, S. Butyrin, S. Somov","doi":"10.1109/STAB49150.2020.9140498","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140498","url":null,"abstract":"The methods for guidance and motion control of a space robot are presented when the visual inspecting the technical state of a geostationary information satellite.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122408069","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 : 2020-06-01DOI: 10.1109/stab49150.2020.9140538
{"title":"STAB 2020 Table of Contents","authors":"","doi":"10.1109/stab49150.2020.9140538","DOIUrl":"https://doi.org/10.1109/stab49150.2020.9140538","url":null,"abstract":"","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115509788","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 : 2020-06-01DOI: 10.1109/stab49150.2020.9140652
{"title":"STAB 2020 Topics of the Conference","authors":"","doi":"10.1109/stab49150.2020.9140652","DOIUrl":"https://doi.org/10.1109/stab49150.2020.9140652","url":null,"abstract":"","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126899367","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 : 2020-06-01DOI: 10.1109/STAB49150.2020.9140542
Y. Sachkov
We consider a one-parameter family of left-invariant rank 2 sub-Finsler problems on the Engel group with the set of control parameters given by a square centered at the origin and rotated by an arbitrary angle. We describe the phase portrait for bang-bang extremals. Further, we obtain an upper bound on the number of bang arcs on optimal bang-bang extremals.
{"title":"Bang-Bang Extremals in Sub-Finsler Problems on Engel Group","authors":"Y. Sachkov","doi":"10.1109/STAB49150.2020.9140542","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140542","url":null,"abstract":"We consider a one-parameter family of left-invariant rank 2 sub-Finsler problems on the Engel group with the set of control parameters given by a square centered at the origin and rotated by an arbitrary angle. We describe the phase portrait for bang-bang extremals. Further, we obtain an upper bound on the number of bang arcs on optimal bang-bang extremals.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114493910","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 : 2020-06-01DOI: 10.1109/STAB49150.2020.9140522
I. Stepanova, A. Salnikov, Alexey Batov
The paper discusses a new block method for solving ill-conditioned systems of linear algebraic equations of large and extra-large dimensions. Systems of this kind often arise in inverse problems of geophysics and geodesy.
{"title":"Variable Dimension Block Method for Solving the Big Data Problem in Geophysics","authors":"I. Stepanova, A. Salnikov, Alexey Batov","doi":"10.1109/STAB49150.2020.9140522","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140522","url":null,"abstract":"The paper discusses a new block method for solving ill-conditioned systems of linear algebraic equations of large and extra-large dimensions. Systems of this kind often arise in inverse problems of geophysics and geodesy.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"270 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122113235","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 : 2020-06-01DOI: 10.1109/STAB49150.2020.9140715
A. S. Kuleshov
In 1890 W. Hess found new partial case of integrability of Euler – Poisson equations describing the motion of a heavy rigid body about a fixed point. In 1892 P. A. Nekrasov proved that the solution of the problem of motion of a heavy rigid body with a fixed point in a Hess case is reduced to integration the second order linear differential equation. In this paper the derive the corresponding linear differential equation and present its coefficients in the rational form. Using the Kovacic algorithm we proved that the liouvillian solutions of the corresponding second order linear differential equation exists only in the case, when the moving rigid body is a Lagrange top, or in the case when the constant of the area integral is zero.
1890年，W。赫斯发现了描述重刚体绕固定点运动的欧拉-泊松方程可积性的部分新情况。1892年P. a . Nekrasov证明了在Hess情况下带不动点的重刚体运动问题的解可以简化为二阶线性微分方程的积分。本文导出了相应的线性微分方程，并将其系数以有理形式表示出来。利用Kovacic算法证明了相应的二阶线性微分方程的liouvillian解仅在运动刚体为拉格朗日顶或面积积分常数为零的情况下才存在。
{"title":"Application of the Kovacic Algorithm to the Problem of Motion of a Heavy Rigid Body with a Fixed Point in a Hess Case","authors":"A. S. Kuleshov","doi":"10.1109/STAB49150.2020.9140715","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140715","url":null,"abstract":"In 1890 W. Hess found new partial case of integrability of Euler – Poisson equations describing the motion of a heavy rigid body about a fixed point. In 1892 P. A. Nekrasov proved that the solution of the problem of motion of a heavy rigid body with a fixed point in a Hess case is reduced to integration the second order linear differential equation. In this paper the derive the corresponding linear differential equation and present its coefficients in the rational form. Using the Kovacic algorithm we proved that the liouvillian solutions of the corresponding second order linear differential equation exists only in the case, when the moving rigid body is a Lagrange top, or in the case when the constant of the area integral is zero.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115286548","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 : 2020-06-01DOI: 10.1109/STAB49150.2020.9140653
Yu. M. Okunev, O. Privalova, V. Samsonov
Descent of a finned body in resisting medium is studied. Two different kinds of blades are discussed: disk and rectangle. Trajectories of a center of mass of a body are analyzed. Two kinds of steady regimes are revealed depending on pitch angles of blades: descent with autorotation and descent with zero angular speed of the body. Dependence of speed of the center of mass on values of pitch angles is described.
{"title":"Influence of shape of blades upon descent of a finned body in media","authors":"Yu. M. Okunev, O. Privalova, V. Samsonov","doi":"10.1109/STAB49150.2020.9140653","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140653","url":null,"abstract":"Descent of a finned body in resisting medium is studied. Two different kinds of blades are discussed: disk and rectangle. Trajectories of a center of mass of a body are analyzed. Two kinds of steady regimes are revealed depending on pitch angles of blades: descent with autorotation and descent with zero angular speed of the body. Dependence of speed of the center of mass on values of pitch angles is described.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125418774","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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