Pub Date : 2023-12-21DOI: 10.1134/s0005117923090047
V. A. Mozzhechkov
Abstract
The problem of static feedback design in linear discrete time-invariant control systems is considered. The desired behavior of the system is defined by a set of its output variation laws (training examples) and by a requirement to the degree of its stability. Controller’s structural constraints are taken into account. Explicit relations are obtained and an iterative method based on these relations is proposed to find a good initial approximation of the desired gain matrix and to refine it sequentially. In the general case, simple-structure gain matrices are found: in such matrices, only those components are nonzero that are necessary and sufficient to give the system the desired properties. Some examples are provided to illustrate the method.
{"title":"Static Feedback Design in Linear Discrete-Time Control Systems Based on Training Examples","authors":"V. A. Mozzhechkov","doi":"10.1134/s0005117923090047","DOIUrl":"https://doi.org/10.1134/s0005117923090047","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The problem of static feedback design in linear discrete time-invariant control systems is considered. The desired behavior of the system is defined by a set of its output variation laws (training examples) and by a requirement to the degree of its stability. Controller’s structural constraints are taken into account. Explicit relations are obtained and an iterative method based on these relations is proposed to find a good initial approximation of the desired gain matrix and to refine it sequentially. In the general case, simple-structure gain matrices are found: in such matrices, only those components are nonzero that are necessary and sufficient to give the system the desired properties. Some examples are provided to illustrate the method.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139031136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-18DOI: 10.1134/s0005117923080052
M. V. Khlebnikov
Abstract
A novel approach is proposed to suppress bounded exogenous disturbances in linear control systems using a PI controller. The approach is based on reducing the original problem to a nonconvex matrix optimization problem. A gradient method for finding the controller’s parameters is derived and its justification is provided. The corresponding recurrence procedure is rather effective and yields quite satisfactory controllers in terms of engineering performance criteria. This paper continues a series of the author’s research works devoted to the design of feedback control laws from an optimization point of view.
摘要 提出了一种使用 PI 控制器抑制线性控制系统中有界外生干扰的新方法。该方法基于将原始问题简化为非凸矩阵优化问题。推导出了一种寻找控制器参数的梯度方法，并提供了其合理性。相应的递推程序相当有效，在工程性能标准方面产生了相当令人满意的控制器。本文是作者致力于从优化角度设计反馈控制法的一系列研究工作的延续。
{"title":"PI Controller Design for Suppressing Exogenous Disturbances","authors":"M. V. Khlebnikov","doi":"10.1134/s0005117923080052","DOIUrl":"https://doi.org/10.1134/s0005117923080052","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A novel approach is proposed to suppress bounded exogenous disturbances in linear control systems using a PI controller. The approach is based on reducing the original problem to a nonconvex matrix optimization problem. A gradient method for finding the controller’s parameters is derived and its justification is provided. The corresponding recurrence procedure is rather effective and yields quite satisfactory controllers in terms of engineering performance criteria. This paper continues a series of the author’s research works devoted to the design of feedback control laws from an optimization point of view.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138743606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-18DOI: 10.1134/s0005117923080064
M. M. Kogan, A. V. Stepanov
Abstract
This paper develops a novel unified approach to designing suboptimal robust control laws for uncertain objects with different criteria based on a priori information and experimental data. The guaranteed estimates of the γ0, generalized H2, and H∞ norms of a closed loop system and the corresponding suboptimal robust control laws are expressed in terms of solutions of linear matrix inequalities considering a priori knowledge and object modeling data. A numerical example demonstrates the improved quality of control systems when a priori and experimental data are used together.
{"title":"Design of Suboptimal Robust Controllers Based on a Priori and Experimental Data","authors":"M. M. Kogan, A. V. Stepanov","doi":"10.1134/s0005117923080064","DOIUrl":"https://doi.org/10.1134/s0005117923080064","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper develops a novel unified approach to designing suboptimal robust control laws for uncertain objects with different criteria based on a priori information and experimental data. The guaranteed estimates of the γ<sub>0</sub>, generalized <i>H</i><sub>2</sub>, and <i>H</i><sub>∞</sub> norms of a closed loop system and the corresponding suboptimal robust control laws are expressed in terms of solutions of linear matrix inequalities considering a priori knowledge and object modeling data. A numerical example demonstrates the improved quality of control systems when a priori and experimental data are used together.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138744001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-18DOI: 10.1134/s0005117923080088
M. E. Shaikin
Abstract
Integral representations of solutions of linear multiplicatively perturbed differential equations are obtained, the diffusion part of which is bilinear on the state vector and the vector of independent Wiener processes. Equations of such class serve as models of stochastic systems with control functioning under conditions of parametric uncertainty or undesirable influence of external disturbances. The concepts and analytical apparatus of the theory of Lie algebras are used to find integral representations and fundamental matrices of the equations.
{"title":"Resolvents of the Ito Differential Equations Multiplicative with Respect to the State Vector","authors":"M. E. Shaikin","doi":"10.1134/s0005117923080088","DOIUrl":"https://doi.org/10.1134/s0005117923080088","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Integral representations of solutions of linear multiplicatively perturbed differential equations are obtained, the diffusion part of which is bilinear on the state vector and the vector of independent Wiener processes. Equations of such class serve as models of stochastic systems with control functioning under conditions of parametric uncertainty or undesirable influence of external disturbances. The concepts and analytical apparatus of the theory of Lie algebras are used to find integral representations and fundamental matrices of the equations.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138744004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-18DOI: 10.1134/s0005117923080106
I. N. Sinitsyn, Yu. P. Titov
Abstract
The paper considers the modification and application of the ant colony method for the problem of directed enumeration of the values of system parameters when performing calculated multiple calculations. Interaction with the user makes it possible to stop the process of exhaustive enumeration of sets of parameter values, and the application of a modification of the ant colony method will allow us to consider rational sets at early iterations. If the user does not terminate the algorithm, then the proposed modifications allow one to enumerate all solutions using the ant colony method. To modify the ant colony method, a new probabilistic formula and various algorithms of the ant colony method are proposed, allowing for each agent to find a new set of parameter values. The optimal algorithm, according to the research results, is the use of repeated endless cyclic search for a new solution. This modification allows you to consider all solutions, and at the same time, find all the optimal solutions among the first 5% of the considered solutions.
{"title":"Control of Set of System Parameter Values by the Ant Colony Method","authors":"I. N. Sinitsyn, Yu. P. Titov","doi":"10.1134/s0005117923080106","DOIUrl":"https://doi.org/10.1134/s0005117923080106","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper considers the modification and application of the ant colony method for the problem of directed enumeration of the values of system parameters when performing calculated multiple calculations. Interaction with the user makes it possible to stop the process of exhaustive enumeration of sets of parameter values, and the application of a modification of the ant colony method will allow us to consider rational sets at early iterations. If the user does not terminate the algorithm, then the proposed modifications allow one to enumerate all solutions using the ant colony method. To modify the ant colony method, a new probabilistic formula and various algorithms of the ant colony method are proposed, allowing for each agent to find a new set of parameter values. The optimal algorithm, according to the research results, is the use of repeated endless cyclic search for a new solution. This modification allows you to consider all solutions, and at the same time, find all the optimal solutions among the first 5% of the considered solutions.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138744007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-18DOI: 10.1134/s0005117923080040
V. L. Khatskevich
Abstract
Scalar characteristics of continuous processes with fuzzy states—mean and correlation functions—are introduced and studied. Their algebraic properties as well as some properties related to the differentiation and integration of fuzzy functions of a real argument are established. The dependence between the characteristics of a fuzzy signal at the input and output of a dynamic system described by a high-order differential equation with constant coefficients is shown.
{"title":"Continuous Processes with Fuzzy States and Their Applications","authors":"V. L. Khatskevich","doi":"10.1134/s0005117923080040","DOIUrl":"https://doi.org/10.1134/s0005117923080040","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Scalar characteristics of continuous processes with fuzzy states—mean and correlation functions—are introduced and studied. Their algebraic properties as well as some properties related to the differentiation and integration of fuzzy functions of a real argument are established. The dependence between the characteristics of a fuzzy signal at the input and output of a dynamic system described by a high-order differential equation with constant coefficients is shown.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138743770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-18DOI: 10.1134/s000511792308009x
A. M. Tsirlin
Abstract
The relationship between the averaging of functions over time and its averaging over the set of values of the required variables is considered. Optimization problems are studied, the criterion and constraints of which include the averaging of functions or functions of the average values of variables. It is shown that the optimality conditions for these problems have the form of the maximum principle, and their optimal solution in the time domain is a piecewise constant function. A generalization of Carathéodory’s theorem on convex hulls of a function is proved. Optimality conditions are obtained for non-linear programming problems with averaging over a part of the variables and functions depending on the average values of the variables.
{"title":"Generalization of the Carathéodory Theorem and the Maximum Principle in Averaged Problems of Non-Linear Programming","authors":"A. M. Tsirlin","doi":"10.1134/s000511792308009x","DOIUrl":"https://doi.org/10.1134/s000511792308009x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The relationship between the averaging of functions over time and its averaging over the set of values of the required variables is considered. Optimization problems are studied, the criterion and constraints of which include the averaging of functions or functions of the average values of variables. It is shown that the optimality conditions for these problems have the form of the maximum principle, and their optimal solution in the time domain is a piecewise constant function. A generalization of Carathéodory’s theorem on convex hulls of a function is proved. Optimality conditions are obtained for non-linear programming problems with averaging over a part of the variables and functions depending on the average values of the variables.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138745831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-18DOI: 10.1134/s0005117923080027
N. V. Grigor’ev
Abstract
The synthesis of a control law for tracking a target informative path as a new approach to solving the problem of planning a flight experiment for identifying the aerodynamic characteristics of automatically controlled aircraft is proposed. The mathematical statement and the method for solving the synthesis problem are obtained. In the numerical experiment, it is shown that the identification accuracy on the synthesized control can be significantly improved compared to the identification accuracy on the optimal program test signal.
{"title":"Synthesis of Test Control for Identification of Aerodynamic Characteristics of Aircraft","authors":"N. V. Grigor’ev","doi":"10.1134/s0005117923080027","DOIUrl":"https://doi.org/10.1134/s0005117923080027","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The synthesis of a control law for tracking a target informative path as a new approach to solving the problem of planning a flight experiment for identifying the aerodynamic characteristics of automatically controlled aircraft is proposed. The mathematical statement and the method for solving the synthesis problem are obtained. In the numerical experiment, it is shown that the identification accuracy on the synthesized control can be significantly improved compared to the identification accuracy on the optimal program test signal.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138743608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-18DOI: 10.1134/s0005117923080039
S. V. Ivanov, A. I. Kibzun, V. N. Akmaeva
Abstract
The problem of stochastic programming with a quantile criterion for a normal distribution is studied in the case of a loss function that is piecewise linear in random parameters and convex in strategy. Using the confidence method, the original problem is approximated by a deterministic minimax problem parameterized by the radius of a ball inscribed in a confidence polyhedral set. The approximating problem is reduced to a convex programming problem. The properties of the measure of the confidence set are investigated when the radius of the ball changes. An algorithm is proposed for finding the radius of a ball that provides a guaranteeing solution to the problem. A method for obtaining a lower estimate of the optimal value of the criterion function is described. The theorems are proved on the convergence of the algorithm with any predetermined probability and on the accuracy of the resulting solution.
{"title":"Parametric Algorithm for Finding a Guaranteed Solution to a Quantile Optimization Problem","authors":"S. V. Ivanov, A. I. Kibzun, V. N. Akmaeva","doi":"10.1134/s0005117923080039","DOIUrl":"https://doi.org/10.1134/s0005117923080039","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The problem of stochastic programming with a quantile criterion for a normal distribution is studied in the case of a loss function that is piecewise linear in random parameters and convex in strategy. Using the confidence method, the original problem is approximated by a deterministic minimax problem parameterized by the radius of a ball inscribed in a confidence polyhedral set. The approximating problem is reduced to a convex programming problem. The properties of the measure of the confidence set are investigated when the radius of the ball changes. An algorithm is proposed for finding the radius of a ball that provides a guaranteeing solution to the problem. A method for obtaining a lower estimate of the optimal value of the criterion function is described. The theorems are proved on the convergence of the algorithm with any predetermined probability and on the accuracy of the resulting solution.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-01DOI: 10.1134/s0005117923120068
Abstract
This paper considers the set of reversible mechanical systems with single-period oscillations and individual phase shifts in them. The problem of aggregating a coupled system with an attracting cycle is solved. The approach developed below is to choose a leader (control) system that acts on the other (follower) systems through one-way coupling control: in an aggregated system, there are no links between follower systems. Universal coupling controls are used. Particular attention is paid to conservative systems. Possible scenarios for the operation of the aggregated system are presented.
{"title":"An Attracting Cycle in a Coupled Mechanical System with Phase Shifts in Subsystem Oscillations","authors":"","doi":"10.1134/s0005117923120068","DOIUrl":"https://doi.org/10.1134/s0005117923120068","url":null,"abstract":"<span> <h3>Abstract</h3> <p>This paper considers the set of reversible mechanical systems with single-period oscillations and individual phase shifts in them. The problem of aggregating a coupled system with an attracting cycle is solved. The approach developed below is to choose a leader (control) system that acts on the other (follower) systems through one-way coupling control: in an aggregated system, there are no links between follower systems. Universal coupling controls are used. Particular attention is paid to conservative systems. Possible scenarios for the operation of the aggregated system are presented.</p> </span>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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