Pub Date : 2020-06-01DOI: 10.1109/STAB49150.2020.9140718
Alexey Pavlovich Mashtakov
We consider the sub-Riemannian problem on the group of rigid body motions in three–dimensional space. Such a problem is encountered in the analysis of 3D images as well as in describing the motion of a solid body in a fluid. Mathematically, this problem reduces to solving a Hamiltonian system, the vertical part of which is a system of six differential equations with unknown functions — extremal controls. We derive an ordinary differential equation for one of the components of the extremal control vector. The obtained equation admits a solution in elliptic functions. Then we find the expression in the operator form for the remaining components of the extremal control vector.
{"title":"On Extremal Controls in the Sub-Riemannian Problem on the Group of Rigid Body Motions","authors":"Alexey Pavlovich Mashtakov","doi":"10.1109/STAB49150.2020.9140718","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140718","url":null,"abstract":"We consider the sub-Riemannian problem on the group of rigid body motions in three–dimensional space. Such a problem is encountered in the analysis of 3D images as well as in describing the motion of a solid body in a fluid. Mathematically, this problem reduces to solving a Hamiltonian system, the vertical part of which is a system of six differential equations with unknown functions — extremal controls. We derive an ordinary differential equation for one of the components of the extremal control vector. The obtained equation admits a solution in elliptic functions. Then we find the expression in the operator form for the remaining components of the extremal control vector.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"10 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":"129846938","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/STAB49150.2020.9140704
N. Sedova, O. Druzhinina
The possibility is studied of reducing the stabilization problem for delay differential nonlinear system to optimization problems with known numerical procedures for solving. Assuming a triangular structure of the system, algorithms are proposed for constructing a stabilizing control. The description of the subsystems in the form of Takagi–Sugeno models is used. Given the state and control constraints, as well as the properties of weight functions, the stabilization problem is reduced to some optimization problems, including LMIs. The obtained controls retain stabilizing properties for non-stationary weight functions, as well as for perturbed systems. Chances of numerical implementation of algorithms based on standard procedures of computational software are considered.
{"title":"Stabilization of Constrained Nonlinear Triangular Delay Systems Using Convex Optimization","authors":"N. Sedova, O. Druzhinina","doi":"10.1109/STAB49150.2020.9140704","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140704","url":null,"abstract":"The possibility is studied of reducing the stabilization problem for delay differential nonlinear system to optimization problems with known numerical procedures for solving. Assuming a triangular structure of the system, algorithms are proposed for constructing a stabilizing control. The description of the subsystems in the form of Takagi–Sugeno models is used. Given the state and control constraints, as well as the properties of weight functions, the stabilization problem is reduced to some optimization problems, including LMIs. The obtained controls retain stabilizing properties for non-stationary weight functions, as well as for perturbed systems. Chances of numerical implementation of algorithms based on standard procedures of computational software are considered.","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":"131713872","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/STAB49150.2020.9140581
A. Galyaev, P. Lysenko
The work is devoted to the study of the phenomenon of synchronization of a large number of weakly coupled oscillators in the presence of dissipative bonds. These bonds are included in the system dynamics equations in the form of diffusion matrices, providing asymptotically stable oscillation of the oscillator ensemble as a whole. Three types of interaction known as "identical all-to-all", "nearest neighbors" and "nearest neighbors in a circle" are considered as examples.
{"title":"About Synchronization Problem of Group of Weakly Coupled Identical Oscillators","authors":"A. Galyaev, P. Lysenko","doi":"10.1109/STAB49150.2020.9140581","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140581","url":null,"abstract":"The work is devoted to the study of the phenomenon of synchronization of a large number of weakly coupled oscillators in the presence of dissipative bonds. These bonds are included in the system dynamics equations in the form of diffusion matrices, providing asymptotically stable oscillation of the oscillator ensemble as a whole. Three types of interaction known as \"identical all-to-all\", \"nearest neighbors\" and \"nearest neighbors in a circle\" are considered as examples.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"42 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":"131219775","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/STAB49150.2020.9140679
D. Rumyantsev, K. Tsarkov
Here we study a number of examples, which establish the fact that well-known certainty equivalence property is not hold for a generalization of LQ decentralized control problem – information constrained problem – even when certainty equivalence principle gives a critical point in the problem, and the admissible control set contains linear controllers only.
{"title":"On Certainty Equivalence Property in Deterministic LQ-problems with Random Initial Data and Information Constraints","authors":"D. Rumyantsev, K. Tsarkov","doi":"10.1109/STAB49150.2020.9140679","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140679","url":null,"abstract":"Here we study a number of examples, which establish the fact that well-known certainty equivalence property is not hold for a generalization of LQ decentralized control problem – information constrained problem – even when certainty equivalence principle gives a critical point in the problem, and the admissible control set contains linear controllers only.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"53 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":"130228695","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/STAB49150.2020.9140529
D. Krasnov
For nonlinear single-channel systems with unmatched disturbances that can be represented in a triangular "input – output" form, a decomposition procedure for the synthesis of dynamic feedback is developed within the framework of the block approach. The procedure involves the synthesis of discontinuous control, providing tracking of the output variable of the command signal under the assumption of the smoothness of external influences; synthesis of a lower-order high-gain observer, which, based on measurements of the tracking error, estimates a mixed variable by which feedback is formed.
{"title":"Dynamic Feedback Synthesis in Tracking Single-Channel Systems under the Influence of Uncontrolled Disturbances","authors":"D. Krasnov","doi":"10.1109/STAB49150.2020.9140529","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140529","url":null,"abstract":"For nonlinear single-channel systems with unmatched disturbances that can be represented in a triangular \"input – output\" form, a decomposition procedure for the synthesis of dynamic feedback is developed within the framework of the block approach. The procedure involves the synthesis of discontinuous control, providing tracking of the output variable of the command signal under the assumption of the smoothness of external influences; synthesis of a lower-order high-gain observer, which, based on measurements of the tracking error, estimates a mixed variable by which feedback is formed.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"11 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":"130373444","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/STAB49150.2020.9140605
V. Poliakov, V. Saurin
The paper discusses the problem of optimal design (stationary optimal control) for multi body dynamic system. The system includes a train and track superstructure interacting with a beam bridge. It is regarded that the speed of the train can reach 400 km/h. The problem of optimal stiffness distribution for continual subsystem – rail bed – is considered. The aim of the optimization is decreasing of irregularity of rail bed loading under constraint on minimal vertical wheel-rail contact force that prevents derailment.
{"title":"The stationary optimal control in combined discrete and continuous system","authors":"V. Poliakov, V. Saurin","doi":"10.1109/STAB49150.2020.9140605","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140605","url":null,"abstract":"The paper discusses the problem of optimal design (stationary optimal control) for multi body dynamic system. The system includes a train and track superstructure interacting with a beam bridge. It is regarded that the speed of the train can reach 400 km/h. The problem of optimal stiffness distribution for continual subsystem – rail bed – is considered. The aim of the optimization is decreasing of irregularity of rail bed loading under constraint on minimal vertical wheel-rail contact force that prevents derailment.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"42 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":"124777421","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/stab49150.2020.9140523
Evgeniy Serafimovich Pyatnitskiy
By the end of 1980-ies Pyatnitskiy conceived an idea to gather scientists of all leading schools specialized in the stability theory. Pyatnitskiy proposed to organize a forum where scientists could present their new results, exchange ideas, discuss the future directions of the development of the stability theory. It was then that the Workshop ‘Stability and Oscillation of Nonlinear Control Systems’ was born. Now scientists who take part in the Workshop regularly call it just ‘Pyatnitskiy’s conference’.
{"title":"Pyatnitskiy’s Conference","authors":"Evgeniy Serafimovich Pyatnitskiy","doi":"10.1109/stab49150.2020.9140523","DOIUrl":"https://doi.org/10.1109/stab49150.2020.9140523","url":null,"abstract":"By the end of 1980-ies Pyatnitskiy conceived an idea to gather scientists of all leading schools specialized in the stability theory. Pyatnitskiy proposed to organize a forum where scientists could present their new results, exchange ideas, discuss the future directions of the development of the stability theory. It was then that the Workshop ‘Stability and Oscillation of Nonlinear Control Systems’ was born. Now scientists who take part in the Workshop regularly call it just ‘Pyatnitskiy’s conference’.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"10 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":"123641849","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/STAB49150.2020.9140586
N. Pavlova, Z. Zhukovskaya, S. Zhukovskiy
The existence of equilibrium price vector functions in continuous dynamic models of the market is studied. The sufficient conditions for the existence of the equilibrium in such models are obtained as corollaries of the existence theorems for coincidence points of covering and Lipschitz continuous mappings acting in metric spaces.
{"title":"Equilibrium in continuous dynamic market models","authors":"N. Pavlova, Z. Zhukovskaya, S. Zhukovskiy","doi":"10.1109/STAB49150.2020.9140586","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140586","url":null,"abstract":"The existence of equilibrium price vector functions in continuous dynamic models of the market is studied. The sufficient conditions for the existence of the equilibrium in such models are obtained as corollaries of the existence theorems for coincidence points of covering and Lipschitz continuous mappings acting in metric spaces.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"84 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":"123932351","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/STAB49150.2020.9140587
O. Anashkin, O. Yusupova
Impulsive differential equations demonstrate rather more complex behavior of solutions than ordinary differential equations. This complexity is due to discontinuities of the integral curves at the moments of impulse actions. We consider a periodic impulsive system in the critical case, when the monodromy matrix of the linear approximation of the system at an equilibrium point has a pair of complex conjugate multipliers on the unit circle. An algorithm for computing of the first Lyapunov value is proposed.
{"title":"Sufficient conditions for stability of the equilibrium position of an impulsive system","authors":"O. Anashkin, O. Yusupova","doi":"10.1109/STAB49150.2020.9140587","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140587","url":null,"abstract":"Impulsive differential equations demonstrate rather more complex behavior of solutions than ordinary differential equations. This complexity is due to discontinuities of the integral curves at the moments of impulse actions. We consider a periodic impulsive system in the critical case, when the monodromy matrix of the linear approximation of the system at an equilibrium point has a pair of complex conjugate multipliers on the unit circle. An algorithm for computing of the first Lyapunov value is proposed.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"46 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":"128029669","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/STAB49150.2020.9140469
G. Alferov, P. Efimova, V. Korolev, D. Shymanchuk
The article describes the approach to remote control of a space robot with force feedback developed by F. M. Kulakov. This method allows to minimize the effect of delays in signal transmission due to features in the control algorithm. Using of feedback on force is necessary for the interaction space robot with objects having holonomic constraints, which is typical for assembly operations. The article gives a mathematical description of the elements of the bilateral control system and also presents a special case of the motion of the robotic system.
本文介绍了F. M. Kulakov开发的空间机器人力反馈远程控制方法。这种方法允许最小化由于控制算法中的特征而导致的信号传输延迟的影响。空间机器人与具有完整约束的物体的相互作用是装配操作中典型的问题，在这种情况下，必须使用力反馈。本文给出了双边控制系统的数学描述，并给出了机器人系统运动的一个特例。
{"title":"Kulakov’s Method of Bilateral Remote Control of a Space Manipulation Robots","authors":"G. Alferov, P. Efimova, V. Korolev, D. Shymanchuk","doi":"10.1109/STAB49150.2020.9140469","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140469","url":null,"abstract":"The article describes the approach to remote control of a space robot with force feedback developed by F. M. Kulakov. This method allows to minimize the effect of delays in signal transmission due to features in the control algorithm. Using of feedback on force is necessary for the interaction space robot with objects having holonomic constraints, which is typical for assembly operations. The article gives a mathematical description of the elements of the bilateral control system and also presents a special case of the motion of the robotic system.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"6 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":"128126794","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：