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## On optimal solutions in a problem with two-dimensional bounded control

P. 90-93.

L.A. Manita, Ronzhina M. I.

We consider an optimal control problem that is affine in two-dimensional control. The origin is a singular trajectory in this problem. We study the structure of optimal solutions in a neighborhood of the origin. We use the resolution of singularity via blow up and the invariant manifold theorems to find a family of optimal solutions.

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

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

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

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

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

Bykadorov I., Ellero A., Moretti E., International Journal of Biomedical Soft Computing and Human Sciences 2013 Vol. 18 No. 1 P. 21-26

We consider a linear optimal control model for the marketing of seasonal products which are produced by the same firm and sold by retailers in different market segments. The horizon is divided in two consecutive non-intersecting intervals, called production and selling periods, respectively. The production period state variables are the inventory levels and two kinds of goodwills (consumers' ...

Added: October 18, 2014

Kashtanov V., , in : Analytical and computational methods in probability theory and its applications (ACMPT-2017). Proceedings of the International Scientific Conference. : M. : RUDN, 2017. P. 26-30.

The functionals constructed on trajectories of the controlled semi- Markov process with a finite set of states are investigated. Theorems of functionals’ structure (dependences on the probability measures defining the Markov homogeneous randomized strategy of control) and of structure of probability measures on which the extremum of these functionals is reached, are formulated. Examples are ...

Added: December 17, 2017

[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

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

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

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

Trautmann P., Vexler B., Zlotnik A., Finite element error analysis for measure-valued optimal control problems governed by a 1D wave equation with variable coefficients / 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

Lancaster : DEStech Publications,Inc., 2018

This volume contains refereed proceedings of the IX International Conference Optimization and Applications (OPTIMA 2018) held in Petrovac, Montenegro, October 1–5, 2018. The previous conferences during 2009–2017 years attracted a significant number of students, researchers, academics, and engineers working in the field of optimization theory, methods, software, and related areas. The Conference was organized by ...

Added: June 5, 2019

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

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

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

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

Azhmyakov V., Trujillo L. A., Italian Journal of Pure and Applied Mathematics 2017 Vol. 2017 No. 37 P. 219-237

This paper deals with a constrained LQ-type optimal control problem (OCP) in the presence of fixed levels input restrictions. We consider control processes governed by linear differential equations with a priori known control switching structure. The set of admissible inputs reflects some important natural engineering applications and moreover, can also be interpreted as a result ...

Added: October 30, 2021

Afanasiev V., , in : ICNPAA 2012 World Congress: 9-th International Conference on Mathematical Problem in Engineering, Aerospace and Science. Vol. 1493.: NY : American Institute of Physics, 2012. P. 13-20.

An optimal control problem is formulated for a class of nonlinear systems for which there exists a coordinate representation 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 on ...

Added: December 3, 2012