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15th International Conference on Optimization and Applications, OPTIMA 2024

作者： Gornov, Alexander Anikin, Anton Sorokovikov, Pavel Zarodnyuk, Tatiana Matrosov Institute for System Dynamics and Control Theory of SB RAS Lermontov Str. 134 Irkutsk664033 Russia

ISBN: (纸本)9783031791185

The article discusses a novel approach for optimizing atomic-molecular structures in extra-large clusters, focusing on reducing computational complexity and applying parallel computing techniques. A three-stage computation process is outlined, offering benefits over traditional algorithms by efficiently navigating through multi-extremal optimization challenges. The software, based on this methodology, demonstrated high efficacy in solving complex molecular dynamics problems. When comparing the outcomes with experimental data, no significant deviations from the expected patterns in potential values were detected. The developed three-stage numerical approach proved instrumental in solving optimization tasks for extra-large atomic-molecular systems. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Molecular dynamics

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VOLTERRA MAP AND RELATED RECURRENCES

arXiv

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arXiv 2025年

作者： Svinin, Andrei K. Matrosov Institute for System Dynamics and Control Theory Siberian Branch of Russian Academy of Sciences P.O. Box 292 Irkutsk664033 Russia

In this paper we analyze recent work [10] by Hone, Roberts and Vanhaecke, where the so-called Volterra map was introduced via the Lax equation that looks similar to the Lax representation for the Mumford’s system [21]. This map turns out to be birational and a corresponding dynamical system on an affine space Mg of dimension 3g + 1 was associated with it. This mapping is related to some discrete equation of the order 2g + 1 associated with the Stieltjes continued fraction expansion of a certain function on a hyperelliptic (elliptic) curve of genus g ≥ 1. The authors of the paper provides examples of this equation for the simplest cases g = 1 and g = 2, but for higher values of g, corresponding equation turns out to be too cumbersome to write them out. We present an approach in which the mentioned (2g+1)-order equation can be written out for all values of g ≥ 1 in a compact form. This equation is not new and can be found, for example, in [18]. An essential point in our framework is the use of special class of discrete polynomials which as shown to be closely related to the Stieltjes continued fraction. On the one hand, this allows us to generalize some of the results of the work [10]. On the other hand, many things in this approach can be presented in a more compact and unified form. Ultimately, we believe that this allows us to give a new perspective on this topic. © 2025, CC BY.

关键词： Dynamical systems

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Relationships between heavy metal migration in soils and landslide dynamics under conditions of modern climate change: A case study of Lake Baikal, Olkhon Island

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Science of the Total Environment 2025年 975卷 179285页

作者： Cherkashina, Tatiana Yu. Svetlakov, Artem A. Pellinen, Vadim A. Cherkashin, Evgeny A. Institute of the Earth's Crust Siberian Branch of Russian Academy of Sciences Lermontov St. 128 Irkutsk664033 Russia Matrosov Institute for System Dynamics and Control Theory Siberian Branch of Russian Academy of Sciences Lermontov St. 134 Irkutsk664033 Russia

The problem of studying landslide processes has attracted worldwide attention due to both the increase in human activities. New data for environmental monitoring of the Lake Baikal coast were obtained. The main goal aims to establish relationships between modern climate changes and the landslide process dynamics, as expressed in the assessment of Hg, Pb, Cd contamination levels, the identification of their possible sources and interelemental relationships, as well as the evaluation of some natural factors. Some improvements to previously developed analytical and physical-mechanical techniques have been made, which have enabled to improve some statistical characteristics for the analytical methods, as well as to achieve uniform moisture distribution throughout the tested sample to the specified values. The coastal zone was classified as moderately to heavily contaminated by Hg (2.97) and Pb (2.08) using the Cf method. The EF and Igeo methods indicated that a significant amount of Hg and Pb was probably from anthropogenic sources. The PCA indicated a strong inverse relationship between Hg and Cd (−0.833) in the landslide zone (L3 site) and a perfect positive relationship in the coastal zone (0.992) that suggests different sources and pathways. A change in soil temperature to positive values (from 0.6 to 1.1 °C) leads to an increase in the depth of thawing, which results in a lowering of the permafrost roof. This proves that permafrost rocks influence landslide activation, which in turn leads to migration of heavy metals in the landslide. These conclusions are fully consistent with the main goal of the study and the proposed hypotheses. These findings can help the authorities of the National Parks and other individuals in charge of making decisions regulate the anthropogenic load on the ecosystem of Olkhon Island and generally the Baikal region. © 2025

关键词： Lake pollution

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Symbolic-Numerical Analysis of the Necessary Stability Conditions for the Relative Equilibria of an Orbital Gyrostat

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Journal of Applied and Industrial Mathematics 2020年第2期14卷 213-221页

作者： Banshchikov, A.V. Matrosov Institute for System Dynamics and Control Theory Irkutsk664033 Russia

Abstract: Using the software developed on the basis of the computer algebra system Mathematica,we study the rotational motion along the circular orbit of a satellite-gyrostat in a Newtoniancentral field of forces. The linearized equations of a perturbed motion in the vicinity of the relativeequilibrium of the system are constructed on a computer in symbolic form, and the necessarystability conditions are obtained for the equilibrium. Implementing the parametric analysis of thederived inequalities, we consider one of the cases when the vector of the gyrostatic moment of thesystem lies in one of the planes formed by the principal central axes of inertia. The obtainedstability regions have an analytical form or a graphical representation as 2D images. © 2020, Pleiades Publishing, Ltd.

关键词： Algebra

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Discrete Facility Location in Machine Learning

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Journal of Applied and Industrial Mathematics 2021年第4期15卷 686-710页

作者： Vasilyev, I.L. Ushakov, A.V. Matrosov Institute for System Dynamics and Control Theory Irkutsk664033 Russia

Abstract: Facility location problems form a broad class of optimization problems extremely popularin combinatorial optimization and operations research. In every facility location problem, one mustlocate a set of facilities in order to satisfy the demands of customers so as some certain objectivefunction be optimal. Besides numerous applications in public and private sectors, the problemsare widely used in machine learning. For example, clustering can be viewed as a facility locationproblem where we need to partition a set of customers into clusters assigned to open *** this survey we briefly look at how the ideas and approaches arisen in the field of facilitylocation led to modern, popular machine learning algorithms supported by many data mining andmachine learning software packages. We also review the state-of-the-art of exact methods andheuristics, as well as some extensions of the basic problems and algorithms in applied machinelearning tasks. Note that the main emphasis lies here on discrete facility location problems which,for example, underlie many widely used clustering algorithms (PAM, affinity propagation, etc.).Since the high computational complexity of the conventional facility location-based clusteringalgorithms hinders their application to modern large-scale real-life datasets;we also survey somemodern approaches to implementation of the algorithms for these large data collections. © 2021, Pleiades Publishing, Ltd.

关键词： Clustering algorithms

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BV solutions of rate independent processes driven by impulsive controls

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IFAC-PapersOnLine 2018年第32期51卷 361-366页

作者： Samsonyuk, Olga N. Timoshin, Sergey A. Matrosov Institute for System Dynamics and Control Theory of SB RAS Irkutsk Russia

An extension to discontinuous inputs of bounded variation of the play operator is presented. The motivation for such an extension comes from optimal impulsive control problems with hysteresis. The latter is introduced by means of variational inequalities modeling the action of the play operator on the BV-inputs. Our extension is applied to the graph completions of BV-functions and it allows us to study impulsive control systems characterized by measure-driven differential equations with nonlinear terms of hysteresis type. Some approximation results for impulsive processes are also provided. © 2018

关键词： Process control Differential equations Hysteresis Nonlinear equations Variational techniques Approximation results impulsive Impulsive control systems Impulsive controls Optimal controls Optimal impulsive control Rate independent process Variational inequalities

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Optimality conditions with feedback controls for optimal impulsive control problems

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IFAC-PapersOnLine 2018年第32期51卷 509-514页

作者： Dykhta, Vladimir A. Samsonyuk, Olga N. Matrosov Institute for System Dynamics and Control Theory of SB RAS Irkutsk Russia

This paper concerns with optimal impulsive control problems with trajectories of bounded variation. Necessary optimality conditions based on weakly monotone solutions of the Hamilton Jacobi inequality and feedback controls are discussed. A particular attention is paid to necessary optimality conditions with feedback controls, called Feedback minimum principle. The latter is generalized the corresponding principle for classical optimal control problems and is formulated in terms of Pontryagin Maximum Principle. An example illustrating these results is considered. © 2018

关键词： Feedback control Differential equations Optimal control systems Bounded variations Hamilton Jacobi inequality Impulsive controls Minimum Principles Necessary optimality condition Optimal control problem Optimal impulsive control Optimality conditions

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Dynamic Programming and control Synthesis for Variational Problems with Polynomial Impulses

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IFAC-PapersOnLine 2018年第32期51卷 304-309页

作者： Goncharova, Elena V. Staritsyn, Maxim V. Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences Irkutsk Russia

The paper suggests a framework of control synthesis (feedback) for differential systems driven by nonlinear impulses. We propose a simple but relevant notion of control synthesis and a related concept of sampling solution. For extremal problems stated for input-polynomial systems, we fix two connected issues: establish the dynamic programming principle, including the characterization of the value function and verification theorem (sufficient optimality condition), and design an optimal synthesis procedure. Finally, we discuss a different, to some extent “dual” to the verification theorem, issue — a sufficient condition for non-optimality, — which performs an application of the control synthesis to discarding non-optimal extrema of the impulsive maximum principle. © 2018

关键词： Dynamic programming Feedback Feedback control control synthesis Impulsive controls necessary Optimal controls Sufficient optimality conditions

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On a Class of Impulsive control Problems for Continuity Equations

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IFAC-PapersOnLine 2018年第32期51卷 468-473页

作者： Staritsyn, Maxim V. Pogodaev, Nikolay I. Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of the Russian Academy of Sciences Irkutsk Russia

The talk presents a class of singular control problems for the continuity equation driven by a control-affine vector fields subject to a constraint on the Li-norm of control inputs, ranged in the whole space. Solutions of such distributed systems may occur to be arbitrary close (in a certain natural sense) to discontinuous measure-valued functions, and — as a consequence — related extremal problems are generically ill-posed. In connection with the addressed model, we discuss the following control-theoretical issues: i) relaxation of the tube of solutions in an appropriate coarse topology; ii) representation of generalized (discontinuous in time) solutions in terms of continuous arcs through a discontinuous time reparameterization of the characteristic ordinary differential equation, and iii) a constructive formula for generalized solutions. For the relaxed model, we state an optimal impulsive ensemble control problem and ensure the existence of a minimizer. Finally, we elaborate a conceptual numeric technique for optimal control and exhibit a case study. © 2018

关键词： Topology Ordinary differential equations Vector spaces Continuity equations Distributed systems Generalized solution Impulsive controls Numeric techniques Optimal controls Reparameterization uncertainty

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Robust controllability of Linear Differential-Algebraic Equations with Unstructured Uncertainty

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Journal of Applied and Industrial Mathematics 2018年第3期12卷 519-530页

作者： Petrenko, P.S. Matrosov Institute of System Dynamics and Control Theory ul. Lermontov 134 Irkutsk664033 Russia

We consider the linear stationary systems of ordinary differential equations (ODEs) that are unsolvedwith respect to the derivative of the unknown vector-function and degenerate identically in the domain of definition. These systems are usually called differential-algebraic equations (DAEs). The measure of how a system of DAEs is unsolved with respect to the derivative is an integer which is called the index of the system of DAEs. The analysis is carried out under the assumption of existence of a structural form with separated differential and algebraic subsystems. We investigate the robust controllability of these systems (controllability in the conditions of uncertainty). The sufficient conditions for the robust complete and R-controllability of a system of DAEs with the indices 1 and 2 are obtained. © 2018, Pleiades Publishing, Ltd.

关键词： controllability

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