Навчально-науковий інститут прикладного системного аналізу (НН ІПСА)

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Pursuit differential-difference games with pure time-lag
(American Institute of Mathematical Sciences, 2019-03) Baranovska, Lesia V.
The analytical approach for the 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 the game solution based on the time-delay exponential is proposed at the 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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Quasi-Linear Differential-Deference Game of Approach
(Springer, 2019) Baranovska, Lesia V.
The paper is devoted to the games of approach. We consider a controlled object whose dynamics is described by the linear differential system with a pure time delay or the differential-difference system with commutative matrices in Euclidean space. The approaches to the solutions of these problems are proposed which based on the Method of Resolving Functions and the First Direct Method of L.S. Pontryagin. The guaranteed times of the game termination are found, and corresponding control laws are constructed. The results are illustrated by a model example.