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Transformation of Guidance Problems

The transformation of the given approach problem to the approach problem "in the moment".

Yurii Averboukh, A Transformation of the Control under Uncertainty Problems // arXiv:0902.2556, 2009.

Arxiv.

Ключевые слова: дифференциальные игры, преобразование игровых задач.

Yurii Averboukh, On the problem of guidance of an autonomous conflict-controlled system onto a cylinder set // Cybernetics and Systems Analysis, Volume 44, Number 5, 729-737, DOI: 10.1007/s10559-008-9044-6, 2008.

 

The problem of guidance of a conflict-controlled system onto a cylinder set is considered. This problem is compared with the problem of guidance of a transformed system onto the base of the cylinder at the last moment. It is shown that the problems considered are equivalent. Moreover, the sequences constructed by the programmed iteration method coincide for both problems.

Paper in Pussian

Ключевые слова: differential games, trasnformation of control problem.

Yurii Averboukh, Programmed Iteration Method for the Aiming Problem of Autonomous Conflict Controlled Systems // Differential Equations and Control Processes, 2007, N 1.

 

 

 

The game-theoretical problem of approach is under consideration. The approach problem ``by the moment'' for an autonomous conflict controlled system is transformed to the approach problem ``at the moment'' for a extended system. 
A variant of a programmed iteration method (iteration of stability) is studied. A.G. Chentsov proved that the sequence of sets converge to the set of successful solvability of approach problem. The coincidence of corresponding iterations is proved; therefore the coincidence of successful solvability sets follows. It is established that if the start system satisfy the Isaacs condition then the transformed system satisfy this condition too.

 

Paper in Russian

Ключевые слова: differential games, trasnformation of control problem.

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Map

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Открыть раздел Stackelberg Solutions of Differential Games
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