Linear Discrete Pursuit Game Problem with Total Constraints

Kuchkarov, Atamurat Shamuratovich; Ibragimov, Gafurjan; Sotvoldiev, Akmal

doi:10.1155/2013/840925

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…Many manufacturing facilities and supply chains can be considered discrete event systems (DES), or, what is the same, event-driven systems with a finite discrete state space [3]. There are several formalisms especially suitable for the modeling of DES, such as finite state machines, generalized semi-Markov processes, discrete event system specification (DEVS), or the Petri nets [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Control of Discrete Event Systems by Means of Discrete Optimization and Disjunctive Colored PNs: Application to Manufacturing Facilities

Latorre-Biel

Jiménez‐Macías

Pérez

et al. 2014

Abstract and Applied Analysis

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Artificial intelligence methodologies, as the core of discrete control and decision support systems, have been extensively applied in the industrial production sector. The resulting tools produce excellent results in certain cases; however, the NP-hard nature of many discrete control or decision making problems in the manufacturing area may require unaffordable computational resources, constrained by the limited available time required to obtain a solution. With the purpose of improving the efficiency of a control methodology for discrete systems, based on a simulation-based optimization and the Petri net (PN) model of the real discrete event dynamic system (DEDS), this paper presents a strategy, where a transformation applied to the model allows removing the redundant information to obtain a smaller model containing the same useful information. As a result, faster discrete optimizations can be implemented. This methodology is based on the use of a formalism belonging to the paradigm of the PN for describing DEDS, the disjunctive colored PN. Furthermore, the metaheuristic of genetic algorithms is applied to the search of the best solutions in the solution space. As an illustration of the methodology proposal, its performance is compared with the classic approach on a case study, obtaining faster the optimal solution.

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Section: Introductionmentioning

confidence: 99%

Control of Discrete Event Systems by Means of Discrete Optimization and Disjunctive Colored PNs: Application to Manufacturing Facilities

Latorre-Biel

Jiménez‐Macías

Pérez

et al. 2014

Abstract and Applied Analysis

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“…There are a few papers that study discrete games under total constraints (see, e.g., [14][15][16][19][20][21][22]).…”

Section: Introductionmentioning

confidence: 99%

“…Kuchkarov et al [22] studied a discrete game whose position ( + 1) ∈ R is described by the above equation. Different from the above game, both controls of the players are subjected to total constraints.…”

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 0-Controllability and Pursuit Problems for Linear Discrete Systems Under Total Constraints on Controls

Kuchkarov

Ibragimov

Sotvoldiev

2014

International Conference on Mathematical Sciences and Statistics 2013

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We consider linear discrete control and pursuit game problems. Control vectors are subjected to total constraints, which are discrete analogues of the integral constraint. By definition, (i) the control system is 0-controllable on the whole if there is a control such that the state of the system z(t) = 0 at some step t, (ii) pursuit can be completed if there exists a strategy of the pursuer such that for any strategy of the evader the state of the system y(t) = 0. We obtained sufficient condition for equivalence of 0-controllability and completion of the game from any initial position of the space.

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Linear Discrete Pursuit Game Problem with Total Constraints

Cited by 3 publications

References 9 publications

Control of Discrete Event Systems by Means of Discrete Optimization and Disjunctive Colored PNs: Application to Manufacturing Facilities

Control of Discrete Event Systems by Means of Discrete Optimization and Disjunctive Colored PNs: Application to Manufacturing Facilities

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

On 0-Controllability and Pursuit Problems for Linear Discrete Systems Under Total Constraints on Controls

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