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On a Class of Impulsive control Problems for Continuity Equations

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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The Set of Relative Equilibria of a Stationary Orbital Asymmetric Gyrostat

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Journal of Applied and Industrial Mathematics 2019年第1期13卷 30-35页

作者： Chaikin, S.V. Matrosov Institute of System Dynamics and Control Theory ul. Lermontova 134 Irkutsk664033 Russia

Under consideration is the well-known problem of relative equilibria (an equilibrium position in the orbital coordinate system) of a gyrostat satellite and their dependence on the design parameters. A new geometric approach to the analysis of the set of relative equilibria is developed. It is proposed to determine the relative equilibria in the corresponding three-dimensional Euclidean space using special aggregated parameters of the systemby the coordinates of the intersection points of two pairs of corresponding hyperbolic cylinders with the sphere of the unit radius. It is shown that, for arbitrary values of the gyrostatic moment and other parameters of the system, there are at least eight different relative equilibria. © 2019, Pleiades Publishing, Ltd.

关键词： Orbits

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First Integrals and Periodic Solutions of a system with Power Nonlinearities

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Journal of Applied and Industrial Mathematics 2018年第1期12卷 70-83页

作者： Kosov, A.A. Semenov, E.I. Matrosov Institute for System Dynamics and Control Theory ul. Lermontova 134 Irkutsk664033 Russia

Under consideration is some system of ordinary differential equations with power nonlinearities. These systems are widely used in mathematical biology and chemical kinetics, and can also occur by reduction of more sophisticatedmodels. We formulate conditions on the system parameters which guarantee the existence of first integrals defined by the combinations of power and logarithmic functions of the phase variables. Using the first integrals, we construct periodic solutions for the three-variable systems. A few examples are given illustrating the results. © 2018, Pleiades Publishing, Ltd.

关键词： Ordinary differential equations

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On the Integrability and Stability of Stationary Solutions of the Goryachev–Sretensky Gyrostat

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Journal of Applied and Industrial Mathematics 2023年第3期17卷 557-570页

作者： Kosov, A.A. Semenov, E.I. Matrosov Institute for System Dynamics and Control Theory Siberian BranchRussian Academy of Sciences Irkutsk664033 Russia

Abstract: The equations of motion of the Goryachev–Sretensky gyrostat are studied. All stationarysolutions are found on the invariant set of the zero level of the area integral, and their stability isanalyzed. For the case where the suspension point coincides with the center of mass and theaction of a gyroscopic moment is of a special type, integration by quadratures is performed. © 2023, Pleiades Publishing, Ltd.

关键词： Equations of motion

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On the Qualitative Analysis of the Equations of Motion of a Rigid Body in a Magnetic Field

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Journal of Applied and Industrial Mathematics 2022年第1期16卷 58-69页

作者： Irtegov, V.D. Titorenko, T.N. Matrosov Institute for System Dynamics and Control Theory Siberian BranchRussian Academy of Sciences Irkutsk664033 Russia

Abstract: In the problem on the motion of a rigid body with a fixed point under the influence of amagnetic field generated by the Barnett–London effect as well as potential forces, the particularcases of existence of additional quadratic integrals are presented and the qualitative analysis of theequations of motion of the body is carried out in one of these cases. © 2022, Pleiades Publishing, Ltd.

关键词： Equations of motion

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On Nonconvex Optimization Problems with D.C. Equality and Inequality Constraints

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IFAC-PapersOnLine 2018年第32期51卷 895-900页

作者： Strekalovsky, Alexander S. Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences Irkutsk664033 Russia

The paper addresses the nonconvex nonsmooth optimization problem with the cost function and equality and inequality constraints given by d.c. functions. The original problem is reduced to a problem without constraints with the help of the exact penalization theory. After that, the penalized problem is represented as a d.c. minimization problem without constraints, for which the new mathematical tools under the form of global optimality conditions (GOCs) are developed. The GOCs reduce the nonconvex problem in question to a family of convex (linearized with respect to the basic nonconvexities) problems. In addition, the GOCs are related to some nonsmooth form of the KKT-theorem for the original problem. On the base of the developed theory we propose new numerical methods for local and global search. © 2018

关键词： Constraint theory Cost functions Linearization Numerical methods Optimization equality exact penalty Global optimality conditions Inequality constraint Kkt points linearized problem local serarch

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Rough Paths theory and Impulsive control: A Promising Connection

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IFAC-PapersOnLine 2018年第32期51卷 615-618页

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

This short discussion note is devoted to establishing some connections between the framework of dynamical systems driven by signals of a low regularity (rough differential equations) and the mathematical theory of impulsive control (measure-driven systems), which, as we believe, would essentially enrich one another. More precisely, we attempt to elaborate an impulsive (discontinuous) extension of the theory of rough differential equation for input-affine models with states of unbounded first variation. In the paper, we are focused on a concept of solution for impulsive rough differential equations with vector-valued controls of bounded p-variation, p£ (1,2), and its constructive representation through a (discrete-continuous) Young's integral equation. © 2018

关键词： Integral equations Differential equations Dynamical systems Constructive representation Driven system Impulsive controls Input affine Mathematical theory Rough differential equations Rough paths Vector valued

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Construction and Investigation of Exact Solutions with Free Boundary to a Nonlinear Heat Equation with Source

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Siberian Advances in Mathematics 2020年第2期30卷 91-105页

作者： Kazakov, A.L. Matrosov Institute for System Dynamics and Control Theory Irkutsk 664033 Russian Federation

Abstract: The article is devoted to the construction and investigation of exact solutions with freeboundary to a second-order nonlinear parabolic equation. The solutions belong to the classes ofgeneralized self-similar and generalized traveling waves. Their construction is reduced to Cauchyproblems for second-order ordinary differential equations (ODE), for which we prove existence anduniqueness theorems for their solutions. A qualitative analysis of the ODE is carried out bypassing to a dynamical system and constructing and studying its phase portrait. In addition, wepresent geometric illustrations. © 2020, Allerton Press, Inc.

关键词： exact solution existence theorem nonlinear heat equation with source qualitative analysis of ordinary differential equations thermal wave

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Angular coefficients of the Drell-Yan process across different rapidity and kinematical ranges

arXiv

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arXiv 2025年

作者： Lyubovitskij, Valery E. Zhevlakov, Alexey S. Anikin, Iurii A. Institut für Theoretische Physik Universität Tübingen Auf der Morgenstelle 14 TübingenD-72076 Germany of ANID Fernández Concha 700 Santiago Chile Bogoliubov Laboratory of Theoretical Physics Joint Institute for Nuclear Research Dubna141980 Russia Matrosov Institute for System Dynamics and Control Theory SB RAS Lermontov str. 134 Irkutsk664033 Russia Department of Physics Tomsk State University Tomsk634050 Russia

We present comprehensive analysis of the angular structure of the Drell-Yan process at different rapidity and kinematical ranges using data of the ATLAS, LHCb, and CMS Collaborations at CERN LHC. From theory side we discuss next-to-leading order calculations in the framework of the collinear perturbative QCD and geometrical method. © 2025, CC BY.

关键词： Angular distribution

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