A method of resolving functions for one class of pursuit problems

Authors

  • Леся Валериевна Барановская National Technical University of Ukraine “Kyiv Polytechnic Institute”, Pr. Peremohy 37, Kyiv, Ukraine, 03056, Ukraine https://orcid.org/0000-0003-0024-8180

DOI:

https://doi.org/10.15587/1729-4061.2015.39355

Keywords:

differential pursuit games, differentialdifference equations, a method of resolving functions / a resolving functions method

Abstract

We have considered a pursuit game with one escapee and one pursuer. The managed conflictprocess is describedin the system of differentialdifference equations of a neutral type. Such equations contain an unknownfunction and its derivatives at different points of time and have not been applied in the theory of differential games yet. Effective in solving particular pursuit game tasks is a resolving functions method that is closely related to L. S. Pontryagin’s first direct method and commonly used in regular differential games and differential-difference games of a delayed type. We have devised a modified method of resolving functions for differentialdifference pursuit games of a neutral type. In the pursuit process, there exists a switch-over point that starts the catch time. This proves that the escapee’s errors do not affect the guaranteed time of the game end, which is calculated and set in advanceby the process parameters.The study has revealed adequate conditions for the process parameters that allow finishing the game within the fixed end time.

The class of the known differential pursuit games can be expanded by the formulated pursuit task, whose process is described in the system of differentialdifference equations of a neutral type, and the devised scheme of the resolving functions method. This facilitates further consideration of such processes in the pursuit task with non-fixed time, objects of various inertia, and integral restrictions.

Author Biography

Леся Валериевна Барановская, National Technical University of Ukraine “Kyiv Polytechnic Institute”, Pr. Peremohy 37, Kyiv, Ukraine, 03056

Associate professor, Candidate of physical and mathematical sciences

The department of Mathematical Physics

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Published

2015-04-23

How to Cite

Барановская, Л. В. (2015). A method of resolving functions for one class of pursuit problems. Eastern-European Journal of Enterprise Technologies, 2(4(74), 4–8. https://doi.org/10.15587/1729-4061.2015.39355

Issue

Vol. 2 No. 4(74) (2015): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2015 Леся Валериевна Барановская

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