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Optimal Solutions in a Neighborhood of a Singular Extremal for a Problem with Two-Dimensional Control
P. 94-96.
We consider an optimal control problem that is affine in two-dimensional bounded control. We study a behavior of solutions
in a neighborhood of a singular extremal. We show that there exists optimal spiral-similar solution which attains the
singular point in finite time making a countable number of rotations.
Language:
English
In book
Steklov Mathematical Institute, 2017
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
Manita L., / Cornell University Library. 2014.
We considered the control problem for wireless sensor networks with a single time server node and a large number of client nodes. The cost functional of this control problem accumulates clock synchronization errors in the clients nodes and the energy consumption of the server over some time interval $[0,T]$. For all possible parameter values we ...
Added: August 28, 2014
Manita L., , in : SMTDA 2014 Conference Proceedings. Vol. 3.: SMTDA, 2014. P. 455-468.
Energy-saving optimization is very important for various engineering problems related to modern distributed systems. We consider here a control problem for a wireless sensor network with a single time server node and a large number of client nodes. The problem is to minimize a functional which accumulates clock synchronization errors in the clients nodes and ...
Added: December 11, 2014
L. Manita, Ronzhina M., , in : Оптимальное управление и дифференциальные игры : Материалы Международной конференции, посвященной 110-летиюсо дня рождения Льва Семеновича Понтрягина, Москва, 12–14 декабря 2018 г. : М. : МАКС Пресс, 2018. P. 171-172.
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. ...
Added: May 15, 2020
Manita L., , in : Stochastic Modeling, Data Analysis & Statistical Applications. : ISAST: International Society for the Advancement of Science and Technology, 2015. P. 461-474.
Power consumption, clock synchronization and optimization are very popular topics an analysis of wireless sensor networks. In the present talk we consider a mathematical model related with large scale networks which nodes are equipped with noisy non-perfect clocks. The task of optimal clock synchronization in such networks is reduced to the classical control problem. Its ...
Added: November 2, 2016
Lerman L., Trifonov K., Chaos 2021 Vol. 31 No. 2 Article 023113
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same level of a Hamiltonian, and two non-symmetric heteroclinic orbits permuted by the involution. This is a codimension one structure; therefore, ...
Added: February 6, 2021
E. Yakovlev, Lerman L., Journal of Geometry and Physics 2019 Vol. 135 P. 70-79
A mathematically correct description is presented on the interrelations between the dynamics of divergence free vector fields on an oriented 3-dimensional manifold M and the dynamics of Hamiltonian systems. It is shown that for a given divergence free vector field Xwith a global cross-section there exist some 4-dimensional symplectic manifold M̃⊃M and a smooth Hamilton function H:M̃→R such that for some c∈R one gets M={H=c}and ...
Added: October 22, 2018
Manita L., Borisov V., Zelikin M., Труды Математического института им. В.А. Стеклова РАН 2010 Т. 271 № 0 С. 40-58
For a class of optimal control problems and Hamiltonian systems generated by these problems in the space l 2, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space l 2 forms a fiber bundle with piecewise smooth two-dimensional ...
Added: April 12, 2012
Жеглов А. Б., Osipov D., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2018 Т. 483 № 5 С. 482-484
Lax pairs for linear Hamiltonian systems of differential equations are found in the paper. The first integrals of the system obtained from these Lax pairs are investigated. ...
Added: October 5, 2018
Manita L., Ronzhnina M., / Cornell University. 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