On linear differential games with integral constraints

Чикрий, А. А.; Белоусов, А. И.

doi:10.1134/s0081543810060076

Cited by 30 publications

(15 citation statements)

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“…The advent of the method of resolving functions [26,53,78,81] brought the natural problem of its propagation to the case of integral constraints. Such an attempt was made, in particular, in [64].…”

Section: Krasovskii's Rule Of Extremal Aiming Time Of the First Absomentioning

confidence: 98%

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Developing B. N. Pshenichnyi’s scientific ideas in optimization and mathematical control theory

Сергиенко

Чикрий

2012

Cybern Syst Anal

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The paper overviews the studies initiated by fundamental works of B. N. Pshenichnyi in the field of necessary extremum conditions, numerical optimization methods, optimal control theory, and differential games. Among them are new scientific fields such as processes with fractional derivatives and impulsive control systems.This year marks the 75th anniversary of the birth of B. N. Pshenichnyi, Academician of the National Academy of Sciences (NAS) of Ukraine, a world famous Ukrainian scientist, an expert in mathematics and cybernetics.Boris Nikolaevich Pshenichnyi graduated from the faculty of mechanics and mathematics of the Ivan Franko National University of L'viv, and the most part of his life worked in Kyiv at the V. M. Glushkov Institute of Cybernetics of the NAS of Ukraine. The range of scientific interests of B. N. Pshenichnyi was extraordinary and included network design and graph 157 1060-0396/12/4802-0157

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Section: Krasovskii's Rule Of Extremal Aiming Time Of the First Absomentioning

confidence: 98%

“…Let us dwell on some recent results in the above-mentioned field, related to Belousov's studies [65,66]. Let the game dynamics be specified by a linear differential equation…”

Section: Krasovskii's Rule Of Extremal Aiming Time Of the First Absomentioning

confidence: 99%

Developing B. N. Pshenichnyi’s scientific ideas in optimization and mathematical control theory

Сергиенко

Чикрий

2012

Cybern Syst Anal

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“…In this paper, the Method of Resolving Functions is chosen as the main tool for research, widely used to study conflict-controlled processes of various nature (see [5,7]). The processes with fractional derivatives are studied in (see [8]), game problems of successive convergence are discussed in (see [9]), a general scheme of the method of resolving functions is given in (see [7]), the applied problem of soft meeting is solved in (see [10]), the nonstationary problems are considered in (see [11][12][13][14]), a variant of the matrix resolving functions are proposed in (see [15]), an approach games problem under the failure of controlling devices are considered in (see [16,17]), and in (see [18,19]) the cases of integral constraints on control are examined.…”

Section: Introductionmentioning

confidence: 99%

Quasi-Linear Differential-Deference Game of Approach

Baranovska

2018

Understanding Complex Systems

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The paper is devoted to the games of approach. We consider a controlled object whose dynamics is described by the linear differential system with pure time delay or the differential-difference system with commutative matrices in Euclidean space. The approaches to the solutions of these problems are proposed which based on the Method of Resolving Functions and the First Direct Method of L.S. Pontryagin. The guaranteed times of the game termination are found, and corresponding control laws are constructed. The results are illustrated by a model example.

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“…A large number of works are devoted to differential games where the position of the players changes continuously in time (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]). Zero-sum differential games were first considered in the book of Isaacs [5] who derived the main equation of the theory of differential games.…”

Section: Introductionmentioning

confidence: 99%

An Approach for Solving Discrete Game Problems with Total Constraints on Controls

Raxmonov

Ibragimov

2014

Abstract and Applied Analysis

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We consider a linear pursuit game of one pursuer and one evader whose motions are described by different-type linear discrete systems. Controls of the players satisfy total constraints. Terminal setMis a subset ofℝnand it is assumed to have nonempty interior. Game is said to be completed ifyk-xk∈Mat some stepk. To construct the control of the pursuer, at each stepi, we use positions of the players from step 1 to stepiand the value of the control parameter of the evader at the stepi. We give sufficient conditions of completion of pursuit and construct the control for the pursuer in explicit form. This control forces the evader to expend some amount of his resources on a period consisting of finite steps. As a result, after several such periods the evader exhausted his energy and then pursuit will be completed.

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On linear differential games with integral constraints

Cited by 30 publications

References 1 publication

Developing B. N. Pshenichnyi’s scientific ideas in optimization and mathematical control theory

Developing B. N. Pshenichnyi’s scientific ideas in optimization and mathematical control theory

Quasi-Linear Differential-Deference Game of Approach

An Approach for Solving Discrete Game Problems with Total Constraints on Controls

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