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# Pursuit differential-difference games with pure time-lag

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

• 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.

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

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