Pursuit differential-difference games with pure time-lag

Lesia V. Baranovska

doi:10.3934/dcdsb.2019004

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2019, Volume 24, Issue 3: 1021-1031. Doi: 10.3934/dcdsb.2019004

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Pursuit differential-difference games with pure time-lag

Lesia V. Baranovska^,

National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", 27 Enthuziastiv st., apt.16, 02154, Kyiv, Ukraine

^* Corresponding author
^* Corresponding author

Received: September 30, 2017

Revised: March 31, 2018

Early access: January 2019

Published: January 2019

The author was partially supported by the National Academy of Sciences of Ukraine, project 2275-f

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Abstract

The analytical approach for solution of pursuit differential-difference games with pure time-lag is considered. For the pursuit local problem with the fixed time the scheme of the method of resolving functions and Pontryagin's first direct method are developed. The integral presentation of game solution based on the time-delay exponential is proposed at first time. The guaranteed times of the game termination are found, and corresponding control laws are constructed. Comparison of the times of approach by the method of resolving functions and Pontryagin's first direct method for the initial problem are made.

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Mathematics Subject Classification: Primary: 49N70; Secondary: 49N75.

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