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## Suboptimal Control of Nonlinear Object:Problem of Keeping Tabs on Reference Trajectory

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 Hamilton–Jacoby–Bellman equation (HJB) to the state dependent Riccati equation (SDRE) upon the control synthesis. In thus paper the optimal control problem by nonlinear system in a task of Keeping Tabs on Reference Trajectory we decide in a key of differential game. The presented example illustrates the application of the proposed control method.

Afanasiev V., Окунькова Е. В., Мехатроника, автоматизация, управление 2013 № 5(146) С. 2-5

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 ...

Added: September 21, 2013

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

М. : МАКС Пресс, 2018

Optimal Control and Differential Games. Materials of the International Conference dedicated to the 110th anniversary of Lev Semenovich Pontryagin, Moscow, December 12-14, 2018 ...

Added: December 16, 2018

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

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

T. A. Alexeeva, Kuznetsov N. V., Lobachev M. et al., IFAC-PapersOnLine 2022 Vol. 55 No. 40 P. 157-162

One of the central tasks of macroeconomic analysis is forecasting and control of economic agents’ expectations for key macroeconomic indicators such as inflation, gross domestic product (GDP), prices and others, etc., so that to achieve maximum level of their welfare through monetary and fiscal policy. This problem is solved within the framework of the optimal ...

Added: April 8, 2023

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

Bykadorov I., Ellero A., Moretti E., , in : Rendiconti per gli Studi Economici quantitativi 2000. : Venice : Università Ca’Foscari di Venezia, Dipartimento di Matematica Applicata, 2001. P. 25-39 .

We consider a monopolistic firm that sells seasonal goods. The firm seeks the minimum of the total advertising expenditure during the selling period, given that some previously defined levels of goodwill and sales have to be reached at the end of the period. The only control allowed is on advertising while goodwill and sales levels ...

Added: November 19, 2013

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

Bykadorov I., Ellero A., Funari S. et al., Journal of Optimization Theory and Applications 2009 Vol. 142 No. 1 P. 55-66

We consider optimal control problems with functional given by the ratio of two integrals (fractional optimal control problems). In particular, we focus on a special case with affine integrands and linear dynamics with respect to state and control. Since the standard optimal control theory cannot be used directly to solve a problem of this kind, ...

Added: November 18, 2013

Bykadorov I., Ellero A., Moretti E., RAIRO-Operation Research 2002 Vol. 36 No. 02 P. 109-127

We consider a firm that sells seasonal goods. The firm seeks to reach a fixed level of goodwill at the end of the selling period, with the minimum total expenditure in promotional activities. We consider the linear optimal control problem faced by the firm which can only control the communication expenditure rate; communication is performed ...

Added: November 18, 2013

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

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

Semion A., Качество. Инновации. Образование 2016 № 6 С. 53-67

This thesis aims on task of quadrotor autopilot development. Model of helicopter was formulated using
quaternion algebra and checked on correctness.
The control problem is formulated in the key control differential game with quadratic cost function. The
synthesis of controls which leads to need of Riccati equation solution with parameters depending on
states at rate of object functioning is ...

Added: October 11, 2016

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

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

Каз. : Издательство Казанского государственного технического университета, 2012

Представлены доклады, посвященные актуальным проблемам теории и практики управления сложными динамическими системами, в том числе по методам оптимального управления, теории игр, интеллектному управлению в условиях неопределенности.
Использование опубликованных материалов будет способствовать расширению связей и повышению эффективности отечественных и зарубежных научно-образовательных центров в области управления. ...

Added: January 23, 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

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

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., 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

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