UDC 519.83:517.7
1 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 g.chikrii@gmail.com
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2 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
kvn_ukr@yahoo.com
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SOLVING THE PROBLEM OF SOFT MEETING FOR CONTROLLED
OSCILLATORY SYSTEMS BASED ON THE PRINCIPLE OF TIME STRETCHING
Abstract. The game problem of a soft meeting of controlled oscillating systems, i.e., their simultaneous coincidence of geometric coordinates and velocities, is considered. Applying Pontryagin’s first direct method [1] to solve this problem is impossible since the condition underlying this method is not satisfied. This condition is an instantaneous advantage of the pursuer (the one who strives to achieve this meeting) over the evader (the one who tries to avoid it). In the method, we apply the principle of time stretching, which weakens this condition and makes it possible to terminate the game in a finite time. The paper outlines the problem solution method that employs a certain time-stretching function. Also, an algorithm, variants of constructing the pursuer control, and an example of computer implementation of the convergence process on the plane are provided.
Keywords: differential game, soft meeting, time stretching function, modified Pontryagin’s condition, selection of set-valued mapping.
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