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P. 171–172.
L. Manita, Ronzhina M.
We consider a linear model of a rotating Timoshenko beam. We show that for some initial conditions, the solutions of the minimization problem for the deviation of the beam from the equilibrium state have Fuller singularities.
Ronzhina M., Manita L., , in: Systems Analysis: Modeling and Control: Materials of the International Conference in memory of Academician A.V. Kryazhimskiy, Moscow, January 23–24, 2024. Abstracts.: -, 2024. P. 25–26.
For some class of small-dimensional optimal control problems we found a family of extremals in the form of logarithmic spirals. These extremals reach the singular surface in a finite time, while the control performs an infinite number of rotations around the circle. ...
Added: October 8, 2025
Afanasiev V., Гаража И. А., Труды Института системного анализа Российской академии наук 2025 Т. 75 № 3 С. 80–91
The problem of a zero-sum differential stabilization game with a quadratic performance functional is considered. The control plant, subject to uncontrollable disturbances, is described by a nonlinear ordinary differential
equation. It is known that the synthesis of optimal feedback controls leads to the need to solve a scalar Bellman-Isaacs partial differential equation at the system's operating speed. An algebraic ...
Added: September 29, 2025
Afanasiev V., Автоматика и телемеханика 2025 № 10 С. 3–20
The optimal control of a system’s final state is a fundamental problem that constitutes the core of many optimization tasks. Such problems involve describing the dynamic object, specifying constraints on controls and states, and defining a quality functional, typically a Bolza functional. The necessary optimality conditions for synthesizing the corresponding controls are written as a canonical Euler–Lagrange system with specified ...
Added: September 24, 2025
Скрыпник Д. В., Экономика и математические методы 2019 Т. 55 № 2 С. 24–42
The article shows that actual public expenditure in the period of rapid oil prices growth of the 2000s was
less than the optimal level in Russia. The macroeconomic model of Russian economy is the basis of current
research. The main mechanism of growth in an optimum scenario is associated with the scaling effect
of public expenditure, which increases ...
Added: February 4, 2024
M.: Steklov Mathematical Institute, 2022.
This collection of articles contains materials of the talks presented at the International Conference dedicated to the centenary of the birth of Academician Evgenii Frolovich Mishchenko, Moscow, June 7–9, 2022 ...
Added: January 31, 2023
Semion A., Presnova A., , in: 16th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB).: IEEE, 2022. Ch. 60 P. 1–4.
In this paper algorithm of control synthesis for car active suspension with delays is examined. The problem is formulated in terms of differential games. External perturbation such as road surface unevenness is considered as actions of some opponent. The commonly known model of quarter car active suspension system will be expanded with delays under 0.5s ...
Added: September 13, 2022
Azhmyakov V., Martinez J. C., Poznyak A., Optimal Control Applications and Methods 2016 Vol. 37 No. 5 P. 1035–1055
This paper is devoted to general optimal control problems (OCPs) associated with a family of nonlinear continuous-time switched systems in the presence of some specific control constraints. The stepwise (fixed-level type) control restrictions we consider constitute a common class of admissible controls in many real-world engineering systems. Moreover, these control restrictions can also be interpreted ...
Added: October 30, 2021
Azhmyakov V., Abstract and Applied Analysis 2016 Vol. 2016 Article 2091526
This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real world processes do not present the ...
Added: October 30, 2021
Ronzhnina M., Manita L., Локуциевский Л. В., Успехи математических наук 2021 Т. 76 № 5(461) С. 201–202
В работе изучается гамильтонова система принципа максимума Понтрягина, аффинная по двумерному управлению. В окрестности особой точки найдены некоторые семейства решений. ...
Added: October 1, 2021
Manita L., Ronzhina M., Discrete and Continuous Dynamical Systems - Series B 2022 Vol. 27 No. 6 P. 3325–3343
We study an optimal control problem affine in two-dimensional bounded control, in which there is a singular point of the second order. In the neighborhood of the singular point we find optimal spiral-like solutions that attain the singular point in finite time, wherein the corresponding optimal controls perform an infinite
number of rotations along the circle $S^{1}$.
The ...
Added: June 19, 2021
Ronzhnina M., Manita L., Локуциевский Л. В., Труды Математического института им. В.А. Стеклова РАН 2021 Т. 315 С. 222–236
Рассмотрены гамильтоновы системы, аффинные по двумерному управлению из круга. Исследована структура оптимального синтеза в окрестности особой экстремали второго порядка. Найдено семейство решений в виде логарифмических спиралей, которые совершают счетное число оборотов вокруг особой точки и попадают в нее за конечное время ...
Added: April 13, 2021
Ronzhina M., Manita L., Journal of Physics: Conference Series 2021 Vol. 1740 P. 1–5
We study singularities of optimal solutions in a problem of controlling the Timoshenko beam vibrations. The Timoshenko beam vibrations are described by a system of two coupled hyperbolic equations. Controls are introduced as external bounded forces. We consider the problem of minimizing the mean square deviation of the Timoshenko beam from the equilibrium position. For ...
Added: April 5, 2021
Manita L., Ronzhnina M., / Series arXiv "math". 2019. No. 1909.04708.
In this paper we study an optimal control problem that is affine in two-dimensional bounded control. The problem is related to the stabilization of an inverted spherical pendulum in the vicinity of the upper unstable equilibrium. We find solutions stabilizing the pendulum in a finite time, wherein the corresponding optimal controls perform an infinite number ...
Added: October 16, 2019