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## The fractional Hamilton-Jacobi-Bellman equation

Journal of Applied Nonlinear Dynamics. 2017. Vol. 6. No. 1. P. 45-56.

Veretennikova M., Kolokoltsov V.

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 extensions to the solution of a new pseudo-differential equation which may be called the fractional Hamilton-Jacobi-Bellman equation.

Veretennikova M., Kolokoltsov V., Communications in Applied and Industrial Mathematics 2015 Vol. 6 No. 1 P. 1-18

In this article we study a controlled Continuous Time Random Walk and its position-dependent extensions. We heuristically derive the optimal payoff function equations for their scaling limits. The general equation for the corresponding optimal payoff of the limiting process may be called a fractional Hamilton Jacobi Bellman equation. ...

Added: October 5, 2016

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

Korotayev A., Вестник Института экономики Российской академии наук 2015 № 1 С. 149-162

The 19th century saw an explosive growth of the gap between the “First” and the “Third” World as regards per capita incomes and levels of life that has become to be known as the “Great Divergence”. In the 20th century the Great Divergence continued up to the early 1970s, and then – in the late ...

Added: December 3, 2015

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

Gorshenin A. K., Belousov V. V., Shnourkoff P. V. et al., AIP Conference Proceedings 2015 Vol. 1648, Article number 250007

This paper is devoted to the numerical simulation of stochastic system for inventory management products using controlled semi-Markov process. The results of a special software for the system’s research and finding the optimal control are presented. ...

Added: April 2, 2015

Grinin L. E., Korotayev A., World Futures 2014 Vol. 70 No. 8 P. 515-545

The article offers forecasts of the geopolitical and geo-economic development
of the world in the forthcoming decades. One of the main accusations directed
toward globalization is that it deepens the gap between the developed and developing
countries dooming them to eternal backwardness. The article demonstrates
that the actual situation is very different. It is shown that this is due ...

Added: December 19, 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

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

Shkolnikov M., Kalinin N., Comptes Rendus Mathematique 2016 Vol. 354 No. 2 P. 125-130

We study a sandpile model on the set of the lattice points in a large lattice polygon. A small perturbation ψ of the maximal stable state μ ≡ 3 is obtained by adding extra grains at several points. It appears that the result ψ◦ of the relaxation of ψ coincides with μ almost everywhere; the ...

Added: March 2, 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

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

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

Veretennikova M., Kolokoltsov V., Fractional Differential Calculus Journal 2014 Vol. 4 No. 1 P. 1-30

The purpose is to study the Cauchy problem for non-linear in time and space pseudo-differential equations. These include fractional in time Hamilton-Jacobi-Bellman equations governing the limits of controlled scaled Continuous Time Random Walks. As a preliminary step which is of independent interest we analyse the corresponding linear equation proving its well-posedness and smoothing properties. ...

Added: September 26, 2016

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

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

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

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

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

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

Veretennikov A., Veretennikova E., On convergence of partial derivatives of multivariate Bernstein polynomials / Cornell University. Series "Working papers by Cornell University". 2015.

It is be shown that the sequence of Bernstein polynomials for a function of several variables converges to this function uniformly along with every partial derivative of any order, provided that the latter derivative is well defined and continuous. This may be interesting in some questions of stochastic calculus, in particular, in a methodical proof ...

Added: October 15, 2015

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