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Гарантированное управление нелинейным объектом (на примере ядерного реактора на тяжелой воде)
Мехатроника, автоматизация, управление. 2013. № 5(146). С. 2-5.
Afanasiev V., Окунькова Е. В.
The task of designing the control actions for a heavy water reactor under uncertainty changes its parameters considered in the key differential game. The possibility of representing nonlinear dynamics of the object in the form of a system with parameters depending on the state (State Dependent Coefficients) and quadratic functional qualities allow you to go from having to solve a scalar partial differential equation (the Hamilton-Jacobi-Bellman) to the Riccati equation with parameters depending on the state. Feasible solution obtained by applying the min-max method. The results of mathematical modeling system in the shutdown of a nuclear reactor.
St. Petersburg : -, 2013
Nowadays, production control problems has been widely studied and a lot of valuable approaches have been implemented. Some work addresses the problem of tracking the uncertain demand in case of uncertain production speeds. The uncertainties are described by deterministic inequalities and the performance is analyzed in from of the worst-case scenario. First, simple mathematical models ...
Added: September 23, 2013
Afanasiev V., , in : Preprints of the IFAC Conference on Manufacturing Modelling, Management, and Control MIM ‘2013 June 19 to 21, 2013, Saint Petersburg, Russia. : St. Petersburg : -, 2013. P. 1505-1509.
An optimal control problem is formulated for a class of nonlinear systems which can be presented by system with linear structure and state-depended coefficients (SDC). The system being under the influence of uncontrollable disturbance is supposed. The linearity of the transformed system structure and the quadratic functional make it possible to pass over from the ...
Added: September 23, 2013
Afanasiev V., М. : Либроком/URSS, 2015
Сложность большого количества современных систем управления зачастую не позволяет получить заранее полное описание процессов, протекающих внутри системы, и ее взаимодействия со средой. Как правило, реальные системы описываются нелинейными дифференциальными уравнениями и достаточно часто математические модели систем управления учитывают лишь допустимые области изменения параметров и характеристик отдельных элементов без конкретизации самих этих параметров и характеристик. Указанные ...
Added: October 29, 2014
Afanasiev V., Автоматика и телемеханика 2014
An optimal control problem was formulated for a class of nonlinear systems which can be presented by a system with a linear structure and state-depended coefficients (SDC). The system be under the influence of uncontrollable disturbance is supposed. In this paper, the problem of control uncertain nonlinear object to the desired trajectory is considered using ...
Added: October 29, 2014
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
Afanasiev V., Андрюхина В. М., Проблемы управления 2012 № 3 С. 41-48
The human immunodeficiency virus infection, that causes Acquired Immune Deficiency Syndrome (AIDS), is a dynamic process that can be modeled via differential equations. The paper introduces
a methodological problem of use of modern mathematical and information methods to boost the response of the immune system by means of drug scheduling. The control purpose is to steer ...
Added: March 21, 2013
Afanasiev V., Автоматика и телемеханика 2011 № 4 С. 43-56
The theoretical fundamentals for solving the linear quadratic problems may be some times used to design the optimal control actions for the nonlinear systems. The method relying on the Riccati equation with state-dependent coefficients is promising and rapidly developing tools for design of the nonlinear controllers. The set of possible suboptimal solutions is generated by ...
Added: April 13, 2012
Afanasiev V., Проблемы управления 2015 № 3 С. 12-19
The problem of optimal control for a class of nonlinear objects with uncontrolled bounded disturbances is formulated in the key differential game. For problems with a quadratic quality functional task of searching for the optimal control reduces the need to find solutions to the scalar partial differential equation Hamilton-Jacobi-Isaacs. Finding solutions to this equation in ...
Added: March 28, 2015
Afanasiev V., Semion A., Проблемы управления 2021 № 1 С. 24-35
A differential game of several players is considered as follows. One player (attacker) penetrates some space, and several other players (pursuers) appear simultaneously to intercept the attacker. Upon detecting the pursuers, the attacker tries to evade them. The dynamics of each player are described by a time-invariant linear system of a general type with scalar ...
Added: April 6, 2021
Shnourkoff P. V., Засыпко В. В., Вестник МГТУ 2014 № 4 С. 101-120
В работе продолжается исследование математической задачи оптимального управления, сформулированной на основе закрытой динамической модели трехсекторной экономики, начатое в статье [12]. Состояние системы описывается набором функций удельного капитала в каждом секторе, параметром управления является величина, характеризующая объем удельных инвестиций фондосоздающего сектора, играющего ключевую роль в экономической системе. Решение поставленной задачи оптимального управления основывается на использовании принципа ...
Added: January 30, 2014
Afanasiev V., Известия РАН. Теория и системы управления 2011 Т. 9 № 1 С. 24-31
Quite many engineering problems, problems from ecology, medicine, and social sciences are characterized by the presence of factors bringing uncertainty into the corresponding control systems. Additional difficulties for control action construction arise in the case when the objects are described by nonlinear highorder evolutionary equations. An important subset of these objects consists of the object ...
Added: April 13, 2012
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
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., 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
Trautmann P., Vexler B., Zlotnik A., / Cornell University. Series "Working papers by Cornell University". 2017. No. 1702.00362.
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 in time bilinear ...
Added: February 2, 2017
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: September 21, 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
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
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
Alexeeva T., Kuznetsov N., Mokaev T. et al., IFAC-PapersOnLine 2021 Vol. 54 No. 17 P. 26-31
Irregular fluctuations in economy lead to unpredictable effects and disrupt its stable functioning. Various tools could be used to stabilize irregular dynamics in economic models. For example, to introduce control into the model as an external function, as well as to take into account the internal characteristics of economic agents in the economy under consideration, ...
Added: February 5, 2022
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
Springer International Publishing, 2019
This book constitutes the refereed proceedings of the 9th International Conference on Optimization and Applications, OPTIMA 2018, held in Petrovac, Montenegro, in October 2018.The 35 revised full papers and the one short paper presented were carefully reviewed and selected from 103 submissions. The papers are organized in topical sections on mathematical programming; combinatorial and discrete optimization; optimal control; optimization in ...
Added: January 14, 2019
Afanasiev V., Orlov P., Известия РАН. Теория и системы управления 2011 Т. 50 № 3 С. 13-22
An optimal control problem is formulated for a class of nonlinear systems for which there exists a coordinate representation (diffeomorphism) transforming the original system into a system with a linear main part and a nonlinear feedback. In this case the coordinate transformation significantly changes the form of original quadratic functional. The penalty matrices become dependent ...
Added: April 13, 2012
Kapalin V. I., Шаповалова Н. Е., Промышленные АСУ и контроллеры 2012 № 10 С. 14-17
An algorithm for the design of linear regulators for nonlinear control objects is suggested. The algorithm is based on interpolation technique and state-space method. An example of the suggested design method in MATLAB is given ...
Added: November 29, 2015