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## Singularity of optimal control in the problem of stabilizing a nonlinear inverted spherical pendulum

Journal of Physics: Conference Series. 2019. Vol. 1163. P. 1-6.

Manita L., Ronzhnina M.

We study an optimal control problem for a nonlinear spherical inverted pendulum on a movable base. As the cost functional, the mean-squared deviation of the pendulum from the upper equilibrium is considered, so optimal controls stabilize the pendulum at the unstable upper position. We show that the problem under consideration posses a singular point of the second order and there are spiral-similar solution which attains the singular point in finite time.

Steklov Mathematical Institute, 2017

Added: June 3, 2017

L. Manita, Ronzhina M., Lobachevskii Journal of Mathematics 2017 Vol. 38 No. 5 P. 954-957

We consider a mathematical model of a spherical inverted pendulum on a movable cart. The cart moves on a horizontal plane under the influence of a planar bounded force. We study an optimal control problem related to this model. The control objective is to stabilize the inverted pendulum in the upright equilibrium position. For the ...

Added: September 20, 2017

Trautmann P., Vexler B., Zlotnik A., Mathematical Control and Related Fields 2018 Vol. 8 No. 2 P. 411-449

This work is concerned with the optimal control problems governed by the 1D wave equation with variable coefficients and the control spaces $\mathcal M_T$ of either measure-valued functions $L^2(I,\mathcal M(\Omega))$ or vector measures $\mathcal M(\Omega,L^2(I))$. The cost functional involves the standard quadratic terms and the regularization term $\alpha\|u\|_{\mathcal M_T}$, $\alpha>0$. We construct and study three-level ...

Added: April 8, 2017

Shnourkoff P. V., Засыпко В. В., Вестник МГТУ 2014 № 2 С. 101-115

A mathematical optimal control problem formulated on the basis of the closed-form
dynamic problem of three-sector economy is studied. The system state is described
by a set of functions of specific capital in each sector; the control parameter is the
quantity characterizing a volume of specific investments of the fund-creating sector
playing a key role in the economic system. ...

Added: January 30, 2014

Shnourkoff P. V., Иванов А. В., Дискретная математика 2014 Т. 26 № 1 С. 143-154

В работе рассматривается дискретная стохастическая модель управления запасом некоторого продукта, основанная на использовании управляемого полумарковского процесса. Определены вероятностные характеристики полумарковского процесса, а также характеристики стационарного стоимостного функционала, связанного с этим процессом. В работе установлено, что оптимальной стратегией управления запасом является детерминированная. Получены явные аналитические представления для стационарного функционала, характеризующего качество управления. Задача оптимального управления сведена ...

Added: January 30, 2014

L.A.Manita, Ronzhina M. I., Journal of Mathematical Sciences 2017 Vol. 221 No. 1 P. 137-153

We consider the problem of stabilization of an n-link inverted pendulum on a movable base (cart). A cart is allowed to move along the horizontal axis. A force applied to the cart is considered as a control. The problem is to minimize the mean square deviation of the pendulum from the vertical line. For the linearized ...

Added: January 11, 2017

Alexander P. Afanas’ev, Sergei M. D., Pchelintsev A. et al., Optimization Letters 2018 Vol. V.12 P. 1-11

We present a method for synthesis of optimal control with feedback of nonlinear systems with separated linear part via quadratic criteria. This method is based on a specialmethod of successive approximations, which allows, under standard assumptions, to find optimal control within any finite time interval and to get the procedure of its construction. An example ...

Added: February 14, 2019

M. : [б.и.], 2018

Book include abstracts of reports presented at the IX International Conference on Optimization Methods and Applications "Optimization and applications" (OPTIMA-2018) held in Petrovac, Montenegro, October 1 - October 5, 2018. ...

Added: October 9, 2018

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

Afanasiev V., Presnova A., Automation and Remote Control 2021 Vol. 82 No. 2 P. 245-263

We state an optimal control problem for a class of dynamical systems whose nonlinear objects can be represented as objects with linear structure and state-dependent parameters. The linearity of the structure of the transformed nonlinear system and the quadratic performance functional allow one to move from the need to search for solutions of the Hamilton–Jacobi ...

Added: January 27, 2021

Manita L., Ronzhnina M., On properties of optimal controls for an inverted spherical pendulum / 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

Larissa Manita, Optimal chattering solutions for longitudinal vibrations of a nonhomogeneous bar / Cornell University. Series math "arxiv.org". 2013. No. arXiv:1302.4001.

We consider a control problem for longitudinal vibrations of a nonhomogeneous bar with clamped ends. The vibrations of the bar are controlled by an external force which is distributed along the bar. For the minimization problem of mean square deviation of the bar we prove that the optimal control has an infinite number of switchings ...

Added: February 20, 2013

M. : -, 2015

Proсeedings inсlude abstraсts of reports presented at the VI International Conferenсe on Optimization Methods and Appliсations "Optimization and appliсations" (OPTIMA-2015) held in Petrovaс, Montenegro, September 27 - Oсtober 3, 2015. ...

Added: August 8, 2015

Shnourkoff P. V., Иванов А. В., Вестник МГТУ 2013 № 3 С. 62-87

The stochastic model of inventory control of a certain product, whose volume may take the values within an interval bounded above the belongs to the set of real numbers, is considered and investigated. This model consists of two components. One of them is named a basic process and describes the inventory level in the system ...

Added: January 29, 2014

Veretennikova M., Kolokoltsov V., Journal of Applied Nonlinear Dynamics 2017 Vol. 6 No. 1 P. 45-56

In this paper we initiate the rigorous analysis of controlled Continuous Time Random Walks (CTRWs) and their scaling limits, which paves the way to the real application of the research on CTRWs, anomalous diffusion and related processes. For the first time convergence is proven for payoff functions for controlled scaled CTRWs and their position dependent ...

Added: October 5, 2016

М. : МАКС Пресс, 2017

The collection represents proceedings of the XVIII international conference “Problems of Theoretical Cybernetics” (Penza, 19–23 June, 2017), that is sponsored by Russian Foundation for Basic Research (project N 17-01-20217-г). The conference subject area includes: control systems synthesis, complexity, reliability, and diagnostics; automata; computer languages and programming; graph theory; combinatorics; coding theory; theory of pattern recognition; ...

Added: August 25, 2017

Yu. B. Grishunina, Automation and Remote Control 2015 Vol. 76 No. 3 P. 433-445

Consideration was given to optimization of the queue control strategy in the MlGl1l queuing system where decision about continuing or stopping admission of customers is made at the service completion instants of each customer in compliance with the distribution on the set of decisions depending on the number of customers remaining in the system. The ...

Added: March 18, 2015

[б.и.], 2017

This volume contains proceedings of the 8th International Conference ”Optimization and Applications” (OPTIMA-2017) that was held in Petrovac, Montenegro, during October 2-7, 2017. The Conference brought together researchers and practitioners working in the field of optimization theory, methods, software and related areas. Optimization is now a rapidly growing area in computer science. It is widely ...

Added: November 14, 2017

Manita L., Journal of Physics: Conference Series 2016 Vol. 681 No. 1 P. 012009-1-012009-6

We discuss a class of optimization problems related to stochastic models of wireless sensor networks (WSNs). We consider a sensor network that consists of a single server node and m groups of identical client nodes. The goal is to minimize the cost functional which accumulates synchronization errors and energy consumption over a given time interval. ...

Added: February 4, 2016

Zhukova A., Pospelov I. G., Экономический журнал Высшей школы экономики 2018 Т. 22 № 3 С. 330-361

In this paper, we consider the classical problem of maximizing discounted utility, provided that the moment of the next purchase and receipt of a loan is random (Poisson). The purpose of the study is to take into account the uncertain waiting period for receipt of a credit in consumption decision-making. The model is formulated as ...

Added: January 16, 2019

Kashtanov V., Dlinnova E., Труды Карельского научного центра РАН. Серия 10: Математическое моделирование и информационные технологии 2016 № 8 С. 34-44

A model of system maintenance which ensures secure operation of the system is investigated. To this end, mathematical model of a controlled semi-Markov process with catastrophes is used. The model allows to take into account the features of self-manifestation of failure (the time has an arbitrary distribution) and features of disaster occurrence (the time required ...

Added: February 18, 2017

Switzerland : Springer, 2020

This volume, edited by Yaroslav D. Sergeyev and Dmitri E. Kvasov, contains selectedpeer-reviewed papers from the Third Triennial International Conference and SummerSchool on Numerical Computations: Theory and Algorithms (NUMTA 2019) held inLe Castella–Isola Capo Rizzuto (Crotone), Italy, during June 15–21, 2019.The NUMTA 2019 conference has continued the previous successful editions ofNUMTA that took place in ...

Added: December 8, 2020

Presnova A., Автоматизация. Современные технологии 2018 Т. 72 № 12 С. 563-569

The problem of searching for optimal control of nonlinear systems is indicated. Using the algorithmic method proposed in this paper, suboptimal control of a nonlinear object is constructed. The necessary assumptions are made for using the method of extended linearization. The example demonstrates the work of an algorithmic method for synthesizing suboptimal controls, and compares ...

Added: October 2, 2018

Manita L., Ronzhina M., Journal of Physics: Conference Series 2018 Vol. 955 No. 1 P. 1-6

Optimal control problem for the system of partial differential equations of hyperbolic type is
considered. By using the Fourier method this problem is reduced to the optimal control
problem for the corresponding Fourier coefficients. For some special initial data we prove
the existence of optimal solutions with a countable number of switchings on a finite time
interval and optimal ...

Added: June 17, 2018