A Collection of Test Multiextremal Optimal Control Problems

Gornov, Alexander; Zarodnyuk, Tatiana; Madzhara, Taras I.; Daneeva, Anna V.; Veyalko, Irina

doi:10.1007/978-1-4614-5131-0_16

Cited by 12 publications

(3 citation statements)

References 12 publications

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“…Some works that apply search and genetic algorithms are also well-known [2,7,27,28,30]. The present authors have contributed to the discussion as well [13][14][15]. But unfortunately these efforts have not yet brought about effective algorithms that would be able to solve a wide spectrum of practical problems (see, e.g.…”

Section: Finding Global Extremum In An Optimal Control Problemmentioning

confidence: 96%

The method of uniform monotonous approximation of the reachable set border for a controllable system

et al. 2015

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A numerical method of a two-dimensional non-linear controllable system reachable set boundary approximation is considered. In order to approximate the boundary right piecewise linear closed contours are used: a set of broken lines on a plane. As an application of the proposed technique a method of finding linear functional global extremum is described, including its use for systems with arbitrary dimensionality.

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Section: Finding Global Extremum In An Optimal Control Problemmentioning

confidence: 96%

The method of uniform monotonous approximation of the reachable set border for a controllable system

et al. 2015

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“…Next, the results of the computational experiments on the study of boundary value problems for systems of functional differential equations of pointwise type (FDEPT) using OPTCON-F software will be presented. The software complex OPTCON-F is designed to obtain a numerical solution of boundary value problems, parametric identification problems and optimal control for dynamical systems described by FDEPT [18]. The proposed technology for solving boundary value problems is based on the Ritz method and spline collocation approaches.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Soliton Solutions for the Manhattan Lattice

Beklaryan,

Akopov

2023

Int. J. of Appl. Math.

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The article is devoted to the study of the aggregated model of motion in the Manhattan lattice. For such a model, the existence and uniqueness theorem of a soliton solution is established, the ranges of characteristics for which the statements of the theorem are valid are indicated, and the asymptotics of the possible growth of such solutions are obtained. A complete family of bounded soliton solutions is constructed.

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“…The corresponding software complex (SC) OPTCON-F was implemented in the language under the control of operating systems OS Windows, OS Linux and Mac OS using compilers BCC 5.5 and GCC. SC was designed to obtain a numerical solution of boundary value problems, parametric identification problems and optimal control for dynamical systems described by FDEPT [21].…”

Section: Soliton Solutions Of the Korteweg-de Vries Equation With A Pmentioning

confidence: 99%

On the existence of soliton solutions for systems with a polynomial potential and their numerical realization

Beklaryan¹

2018

JMLDA

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The problem of existence of soliton solutions (solutions of the traveling wave type) for the Korteweg-de Vries equation with a polynomial potential is considered on the basis of the approach within which the presence of a one-to-one correspondence of such solutions with solutions of the induced functional differential equation of pointwise type is demonstrated. On this path, conditions for the existence and uniqueness of solutions of the traveling wave type, with the growth restrictions both in time and in space, arise. It is very important that the conditions for the existence of a traveling wave solution are formed in terms of the right-hand side of the equation and the characteristics of the traveling wave, without using either the linearization and spectral properties of the corresponding equation in variations. Conditions for the existence of periodic soliton solutions are considered separately, and the possibility of transition from systems with a quasilinear potential to systems with a polynomial potential with conservation of corresponding existence theorems is demonstrated. Numerical implementation of such solutions is given.

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A Collection of Test Multiextremal Optimal Control Problems

Cited by 12 publications

References 12 publications

The method of uniform monotonous approximation of the reachable set border for a controllable system

The method of uniform monotonous approximation of the reachable set border for a controllable system

Soliton Solutions for the Manhattan Lattice

On the existence of soliton solutions for systems with a polynomial potential and their numerical realization

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