Pub Date : 2024-09-06DOI: 10.1134/s0005117924050059
E. N. Gryazina, D. Y. Baluev
Abstract
The paper is devoted to the analysis of the feasibility domain of electric power systems. The problems of calculating feasible and marginal regimes of power systems, analyzing the geometry of the feasibility domain, and generating samples in this region are considered. Parallels are drawn with the works of B.T. Polyak on the analysis of the image of a quadratic map, modification of the Newton method and the development of methods for generating asymptotically uniform samples in areas with complex geometry. Particular attention is paid to Newton’s method with the transversality condition (TENR), its application for constructing a boundary oracle procedure and utilization for generating samples in the power system feasibility domain.
摘要 本文致力于分析电力系统的可行性域。文中考虑了计算电力系统的可行和边际制度、分析可行性域的几何形状以及在该区域生成样本等问题。该书与 B.T. Polyak 在二次图象分析、牛顿方法的修改以及在具有复杂几何形状的区域生成渐近均匀样本的方法开发等方面的著作有相似之处。特别关注的是牛顿方法与横向条件（TENR）、其在构建边界甲骨文程序中的应用以及在电力系统可行性领域中生成样本的利用。
{"title":"Investigation of Feasible and Marginal Operating Regimes of Electric Power Systems","authors":"E. N. Gryazina, D. Y. Baluev","doi":"10.1134/s0005117924050059","DOIUrl":"https://doi.org/10.1134/s0005117924050059","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper is devoted to the analysis of the feasibility domain of electric power systems. The problems of calculating feasible and marginal regimes of power systems, analyzing the geometry of the feasibility domain, and generating samples in this region are considered. Parallels are drawn with the works of B.T. Polyak on the analysis of the image of a quadratic map, modification of the Newton method and the development of methods for generating asymptotically uniform samples in areas with complex geometry. Particular attention is paid to Newton’s method with the transversality condition (TENR), its application for constructing a boundary oracle procedure and utilization for generating samples in the power system feasibility domain.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198064","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 : 2024-09-06DOI: 10.1134/s0005117924050035
M. V. Balashov, K. Z. Biglov, A. A. Tremba
Abstract
We consider some problems with a set-valued mapping, which can be reduced to minimization of a homogeneous Lipschitz function on the unit sphere. Latter problem can be solved in some cases with a first order algorithm—the gradient projection method. As one of the examples, the case when set-valued mapping is the reachable set of a linear autonomous controlled system is considered. In several settings, the linear convergence is proven. The methods used in proofs follow those introduced by B.T. Polyak for the case where Lezanski–Polyak–Lojasiewicz condition holds. Unlike algorithms that use approximation of the reachable set, the proposed algorithms depend far less on dimension and other parameters of the problem. Efficient error estimation is possible. Numerical experiments confirm the effectiveness of the considered approach. This approach can also be applied to various set-theoretical problems with general set-valued mappings.
摘要 我们考虑了一些具有集值映射的问题，这些问题可以简化为单位球面上均质 Lipschitz 函数的最小化。在某些情况下，后一个问题可以用一阶算法--梯度投影法来解决。作为例子之一，我们考虑了集值映射是线性自主控制系统可达集的情况。在几种情况下，都证明了线性收敛性。证明中使用的方法沿用了 B.T. Polyak 针对 Lezanski-Polyak-Lojasiewicz 条件成立的情况提出的方法。与使用可达集近似值的算法不同，所提出的算法对问题的维度和其他参数的依赖性要小得多。高效的误差估计是可能的。数值实验证实了所考虑方法的有效性。这种方法也可应用于具有一般集值映射的各种集合理论问题。
{"title":"On Some Problems with Multivalued Mappings","authors":"M. V. Balashov, K. Z. Biglov, A. A. Tremba","doi":"10.1134/s0005117924050035","DOIUrl":"https://doi.org/10.1134/s0005117924050035","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider some problems with a set-valued mapping, which can be reduced to minimization of a homogeneous Lipschitz function on the unit sphere. Latter problem can be solved in some cases with a first order algorithm—the gradient projection method. As one of the examples, the case when set-valued mapping is the reachable set of a linear autonomous controlled system is considered. In several settings, the linear convergence is proven. The methods used in proofs follow those introduced by B.T. Polyak for the case where Lezanski–Polyak–Lojasiewicz condition holds. Unlike algorithms that use approximation of the reachable set, the proposed algorithms depend far less on dimension and other parameters of the problem. Efficient error estimation is possible. Numerical experiments confirm the effectiveness of the considered approach. This approach can also be applied to various set-theoretical problems with general set-valued mappings.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198240","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 : 2024-09-06DOI: 10.1134/s0005117924050023
V. A. Alexandrov
Abstract
The problem of finding the arrangement of closed-loop control system poles that minimizes an objective function is considered. The system optimality criterion is the value of the H∞ norm of the frequency transfer function relative to the disturbance with constraints imposed on the system pole placement and the values of the H∞ norm of the sensitivity function and the transfer function from measurement noise to control. An optimization problem is formulated as follows: the vector of variables consists of the characteristic polynomial roots of the closed loop system with the admissible values restricted to a given pole placement region; in addition to the optimality criterion, the objective function includes penalty elements for other constraints. It is proposed to use a logarithmic scale for the moduli of the characteristic polynomial roots as elements of the vector of variables. The multi-extremality problem of the objective function is solved using the multiple start procedure. A coordinate descent modification with a pair of coordinates varied simultaneously is used for search.
{"title":"An Optimal Choice of Characteristic Polynomial Roots for Pole Placement Control Design","authors":"V. A. Alexandrov","doi":"10.1134/s0005117924050023","DOIUrl":"https://doi.org/10.1134/s0005117924050023","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The problem of finding the arrangement of closed-loop control system poles that minimizes an objective function is considered. The system optimality criterion is the value of the <i>H</i><sub>∞</sub> norm of the frequency transfer function relative to the disturbance with constraints imposed on the system pole placement and the values of the <i>H</i><sub>∞</sub> norm of the sensitivity function and the transfer function from measurement noise to control. An optimization problem is formulated as follows: the vector of variables consists of the characteristic polynomial roots of the closed loop system with the admissible values restricted to a given pole placement region; in addition to the optimality criterion, the objective function includes penalty elements for other constraints. It is proposed to use a logarithmic scale for the moduli of the characteristic polynomial roots as elements of the vector of variables. The multi-extremality problem of the objective function is solved using the multiple start procedure. A coordinate descent modification with a pair of coordinates varied simultaneously is used for search.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198053","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 : 2024-09-06DOI: 10.1134/s0005117924050060
Yu. S. Popkov
Abstract
This paper is devoted to the problem of solving a system of nonlinear equations with an arbitrary but continuous vector function on the left-hand side. By assumption, the values of its components are the only a priori information available about this function. An approximate solution of the system is determined using some iterative method with parameters, and the qualitative properties of the method are assessed in terms of a quadratic residual functional. We propose a self-learning (reinforcement) procedure based on auxiliary Monte Carlo (MC) experiments, an exponential utility function, and a payoff function that implements Bellman’s optimality principle. A theorem on the strict monotonic decrease of the residual functional is proven.
{"title":"Iterative Methods with Self-Learning for Solving Nonlinear Equations","authors":"Yu. S. Popkov","doi":"10.1134/s0005117924050060","DOIUrl":"https://doi.org/10.1134/s0005117924050060","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper is devoted to the problem of solving a system of nonlinear equations with an arbitrary but continuous vector function on the left-hand side. By assumption, the values of its components are the only a priori information available about this function. An approximate solution of the system is determined using some iterative method with parameters, and the qualitative properties of the method are assessed in terms of a quadratic residual functional. We propose a self-learning (reinforcement) procedure based on auxiliary Monte Carlo (MC) experiments, an exponential utility function, and a payoff function that implements Bellman’s optimality principle. A theorem on the strict monotonic decrease of the residual functional is proven.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225226","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 : 2024-09-06DOI: 10.1134/s0005117924050047
A. Glushchenko, K. Lastochkin
Abstract
An adaptive state-feedback control system is proposed for a class of linear time-varying systems represented in the controller canonical form. The adaptation problem is reduced to the one of Taylor series-based first approximations of the ideal controller parameters. The exponential convergence of identification and tracking errors of such an approximation to an arbitrarily small and adjustable neighbourhood of the equilibrium point is ensured if the condition of the regressor persistent excitation with a sufficiently small time period is satisfied. The obtained theoretical results are validated via numerical experiments.
{"title":"Approximation-Based Approach to Adaptive Control of Linear Time-Varying Systems","authors":"A. Glushchenko, K. Lastochkin","doi":"10.1134/s0005117924050047","DOIUrl":"https://doi.org/10.1134/s0005117924050047","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An adaptive state-feedback control system is proposed for a class of linear time-varying systems represented in the controller canonical form. The adaptation problem is reduced to the one of Taylor series-based first approximations of the ideal controller parameters. The exponential convergence of identification and tracking errors of such an approximation to an arbitrarily small and adjustable neighbourhood of the equilibrium point is ensured if the condition of the regressor persistent excitation with a sufficiently small time period is satisfied. The obtained theoretical results are validated via numerical experiments.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198109","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 : 2024-08-23DOI: 10.1134/s0005117924040039
V. L. Khatskevich
Abstract
In this paper, stationary random processes with fuzzy states are studied. The properties of their numerical characteristics—fuzzy expectations, expectations, and covariance functions—are established. The spectral representation of the covariance function, the generalized Wiener–Khinchin theorem, is proved. The main attention is paid to the problem of transforming a stationary fuzzy random process (signal) by a linear dynamic system. Explicit-form relationships are obtained for the fuzzy expectations (and expectations) of input and output stationary fuzzy random processes. An algorithm is developed and justified to calculate the covariance function of a stationary fuzzy random process at the output of a linear dynamic system from the covariance function of a stationary input fuzzy random process. The results rest on the properties of fuzzy random variables and numerical random processes. Triangular fuzzy random processes are considered as examples.
{"title":"On the Transformation of a Stationary Fuzzy Random Process by a Linear Dynamic System","authors":"V. L. Khatskevich","doi":"10.1134/s0005117924040039","DOIUrl":"https://doi.org/10.1134/s0005117924040039","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, stationary random processes with fuzzy states are studied. The properties of their numerical characteristics—fuzzy expectations, expectations, and covariance functions—are established. The spectral representation of the covariance function, the generalized Wiener–Khinchin theorem, is proved. The main attention is paid to the problem of transforming a stationary fuzzy random process (signal) by a linear dynamic system. Explicit-form relationships are obtained for the fuzzy expectations (and expectations) of input and output stationary fuzzy random processes. An algorithm is developed and justified to calculate the covariance function of a stationary fuzzy random process at the output of a linear dynamic system from the covariance function of a stationary input fuzzy random process. The results rest on the properties of fuzzy random variables and numerical random processes. Triangular fuzzy random processes are considered as examples.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198113","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 : 2024-08-23DOI: 10.1134/s0005117924040064
O. B. Tsekhan
Abstract
For a linear time-varying singularly perturbed system with a small parameter μ for a part of derivatives and quasi-differentiable coefficients, existence conditions are established and μ-asymptotic composite full- and reduced-order observers are constructed. The error in estimating a state with an arbitrary predetermined exponential decay rate converges to an infinitesimal value of the same order of smallness as the small parameter. The observer gain vector are expressed in terms of the gain vectors of subsystems of smaller dimension than the original one and independent of the small parameter, and the parameters of the original system are subject to weaker requirements than those previously known. A constructive algorithm for calculating the gain vector of a composite observer is presented.
{"title":"Composite Observer of a Linear Time-Varying Singularly Perturbed System with Quasidifferentiable Coefficients","authors":"O. B. Tsekhan","doi":"10.1134/s0005117924040064","DOIUrl":"https://doi.org/10.1134/s0005117924040064","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>For a linear time-varying singularly perturbed system with a small parameter μ for a part of derivatives and quasi-differentiable coefficients, existence conditions are established and μ-asymptotic composite full- and reduced-order observers are constructed. The error in estimating a state with an arbitrary predetermined exponential decay rate converges to an infinitesimal value of the same order of smallness as the small parameter. The observer gain vector are expressed in terms of the gain vectors of subsystems of smaller dimension than the original one and independent of the small parameter, and the parameters of the original system are subject to weaker requirements than those previously known. A constructive algorithm for calculating the gain vector of a composite observer is presented.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198115","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 : 2024-08-23DOI: 10.1134/s0005117924040076
D. D. Yaparov, A. L. Shestakov
Abstract
A dynamic measuring system is considered. A new model of the measuring system, a method for processing of measurement results and a method of restoring the input signal of the system by the noisy output signal are proposed. The estimation of the accuracy of the method and a computational experiment demonstrating the efficiency of the signal recovery method are presented.
{"title":"Self-Regulating Dynamic Measurement Method","authors":"D. D. Yaparov, A. L. Shestakov","doi":"10.1134/s0005117924040076","DOIUrl":"https://doi.org/10.1134/s0005117924040076","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A dynamic measuring system is considered. A new model of the measuring system, a method for processing of measurement results and a method of restoring the input signal of the system by the noisy output signal are proposed. The estimation of the accuracy of the method and a computational experiment demonstrating the efficiency of the signal recovery method are presented.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227659","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 : 2024-08-23DOI: 10.1134/s0005117924040040
A. V. Pesterev, Yu. V. Morozov
Abstract
Stability of a switching system, which comes to existence when stabilizing a chain of two integrators by a feedback in the form of nested saturators, is studied. The use of the feedback in the form of nested saturators makes it possible to take into account boundedness of the control resource and to ensure the fulfillment of the phase constraint on the velocity of approaching the equilibrium state, which is especially important in the case of large initial deviations. A Lyapunov function is constructed by means of which global asymptotic stability of the closed-loop system is proved for any positive feedback coefficients.
{"title":"Global Stabilization of a Chain of Two Integrators by a Feedback in the Form of Nested Saturators","authors":"A. V. Pesterev, Yu. V. Morozov","doi":"10.1134/s0005117924040040","DOIUrl":"https://doi.org/10.1134/s0005117924040040","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Stability of a switching system, which comes to existence when stabilizing a chain of two integrators by a feedback in the form of nested saturators, is studied. The use of the feedback in the form of nested saturators makes it possible to take into account boundedness of the control resource and to ensure the fulfillment of the phase constraint on the velocity of approaching the equilibrium state, which is especially important in the case of large initial deviations. A Lyapunov function is constructed by means of which global asymptotic stability of the closed-loop system is proved for any positive feedback coefficients.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198107","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 : 2024-08-23DOI: 10.1134/s0005117924040027
D. N. Ibragimov
Abstract
The problem of constructing reachable and null-controllable sets for stationary linear discrete-time systems with a summary constraint on the scalar control is considered. For the case of quadratic constraints and a diagonalizable matrix of the system, these sets are built explicitly in the form of ellipsoids. In the general case, the limit reachable and null-controllable sets are represented as fixed points of a contraction mapping in the metric space of compact sets. On the basis of the method of simple iteration, a convergent procedure for constructing their external estimates with an indication of the a priori approximation error is proposed. Examples are given.
{"title":"On the External Estimation of Reachable and Null-Controllable Limit Sets for Linear Discrete-Time Systems with a Summary Constraint on the Scalar Control","authors":"D. N. Ibragimov","doi":"10.1134/s0005117924040027","DOIUrl":"https://doi.org/10.1134/s0005117924040027","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The problem of constructing reachable and null-controllable sets for stationary linear discrete-time systems with a summary constraint on the scalar control is considered. For the case of quadratic constraints and a diagonalizable matrix of the system, these sets are built explicitly in the form of ellipsoids. In the general case, the limit reachable and null-controllable sets are represented as fixed points of a contraction mapping in the metric space of compact sets. On the basis of the method of simple iteration, a convergent procedure for constructing their external estimates with an indication of the a priori approximation error is proposed. Examples are given.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225227","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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