Conflict-Controlled Processes

Чикрий, А. А.

doi:10.1007/978-94-017-1135-7

Cited by 120 publications

(87 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The proposed method has proved effective for solving classical problems with phase constraints: "cornered rat,'~' "man and lion," "death row game," "patrolling the corridor" [124]. The available conditions of complete conflict controllability in the class of stroboscopic strategies and quasistrategies generalize Kalman's corresponding results.…”

Section: Here S(c X) ~ II (C X) C P(c X) C Xmentioning

confidence: 74%

“…The resolving function method has been used to solve group pursuit and alternating pursuit problems. Sufficient solvability conditions have been obtained for the "encirclement" problem in a finite time [124]. For simple alternating pursuit the locus of capture point has been found, which in particular is the Appolonius circle.…”

Section: Here S(c X) ~ II (C X) C P(c X) C Xmentioning

confidence: 97%

“…Pursuit and evasion games are studied by the method of inverse Minkowski functionals (the resolving function method) [124], which focuses on multivalued mappings of a special form and their selectors. The method is implemented in the class of quasistrategies and, in particular, proves the classical rule of parallel pursuit.…”

Section: Here S(c X) ~ II (C X) C P(c X) C Xmentioning

confidence: 99%

“…Objects with various inertial properties, oscillatory processes [125], and systems with phase constraints [124] have been investigated. In the latter case, the decision functions may take negative values.…”

Section: Here S(c X) ~ II (C X) C P(c X) C Xmentioning

confidence: 99%

See 3 more Smart Citations

Some directions and results of research in mathematical programming and system analysis

Сергиенко¹

1995

Cybern Syst Anal

View full text Add to dashboard Cite

This article reviews the research in informatics, optimization theory, and system analysis associated with the scientific interests of our well-known scientist and mathematician, V. S. Mikhalevich, and his closest students and followers. We should qualify at the outset that the article does not review the full body of work of Mikhalevich, and certainly not of all his students: their work is much too extensive and much too multifaceted for one survey article. Moreover, in optimization theory, for instance, the Kiev mathematical school includes directions represented by other widely known scientists, and again these are not treated in the present article. I have decided to focus only on the studies and the directions of research to which V. S. Mikhalevich attached particular significance, which to a certain extent characterize his scientific creativity, and which are widely acknowledged among experts in our country and abroad.The active development of research in mathematical programming and system analysis at the National Academy of Sciences of Ukraine began in the late 1950s and early 1960s, when the Computational Center of the Academy of Sciences of the Ukrainian SSR and a number of other scientific organizations in the country focused on the creation of new computers and computer software. At that time, Academician V. M. Glushkov organized in Kiev a number of scientific seminars, which served as a starting point for studies in optimization theory, modeling of production processes, and computer-aided design of complex objects. Glushkov was apparently among the first cyberneticists who called attention to the need for the development of methods of system analysis, whose application in conjunction with modern computers to the study of complex processes in economics, medicine, engineering, and military science might achieve the desired goals. At that time, Mikhalevich himself, as well as his students and followers, were beginning their systematic work in this field. Their work was typically motivated by practical needs, and therefore immediately found wide applications for the solution of real-life problems.The studies reviewed in this article can be classified into three main groups: a) development and application of numerical optimization methods; b) informatization of society and issues of economic cybernetics; c) development of multiprocessor computers and computer software.

show abstract

Section: Here S(c X) ~ II (C X) C P(c X) C Xmentioning

confidence: 74%

Section: Here S(c X) ~ II (C X) C P(c X) C Xmentioning

confidence: 97%

Section: Here S(c X) ~ II (C X) C P(c X) C Xmentioning

confidence: 99%

Section: Here S(c X) ~ II (C X) C P(c X) C Xmentioning

confidence: 99%

See 2 more Smart Citations

Some directions and results of research in mathematical programming and system analysis

Сергиенко¹

1995

Cybern Syst Anal

View full text Add to dashboard Cite

show abstract

“…The use of asymptotic representations of these functions in the framework of the Method of Resolving Functions [5,6,7] allows to derive sufficient conditions for solvability of corresponding game problems. These conditions are based on the modified Pontrjagin's condition [5]. The results are illustrated on a model example where a dynamic system of order π pursues another system of order e.…”

Section: Introductionmentioning

confidence: 99%

Riemann–Liouville, Caputo, and Sequential Fractional Derivatives in Differential Games

Чикрий

Matychyn

2010

Annals of the International Society of Dynamic Games

View full text Add to dashboard Cite

There exists a number of definitions of the fractional order derivative. The classical one is the definition by Riemann-Liouville [1]. The RiemannLiouville fractional derivatives have a singularity at zero. That is why differential equations involving these derivatives require initial conditions of special form lacking clear physical interpretation. These shortcomings do not occur with the regularized fractional derivative in the sense of Caputo. Both the Riemann-Liouville and Caputo derivatives possess neither semigroup nor commutative property. That is why so-called sequential derivatives were introduced by Miller and Ross [2].In this paper we treat sequential derivatives of special form [3]. Their relation to the Riemann-Liouville and Caputo fractional derivatives and to each other is established.Differential games for the systems with the fractional derivatives of Riemann-Liouville, Caputo, as well as with the sequential derivatives are studied. Representations of such systems' solutions involving the MittagLeffler generalized matrix functions [4] are given. The use of asymptotic representations of these functions in the framework of the Method of Resolving Functions [5,6,7] allows to derive sufficient conditions for solvability of corresponding game problems. These conditions are based on the modified Pontrjagin's condition [5]. The results are illustrated on a model example where a dynamic system of order π pursues another system of order e.

show abstract

Game Problems for Systems with Fractional Derivatives of Arbitrary Order

Чикрий

Annals of the International Society of Dynamic Games

View full text Add to dashboard Cite

Conflict-Controlled Processes

Cited by 120 publications

References 0 publications

Some directions and results of research in mathematical programming and system analysis

Some directions and results of research in mathematical programming and system analysis

Riemann–Liouville, Caputo, and Sequential Fractional Derivatives in Differential Games

Game Problems for Systems with Fractional Derivatives of Arbitrary Order

Contact Info

Product

Resources

About