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Algorithm of uniform filling of nonlinear dynamic system reachable set based on maximin problem solution

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Abstract

In this paper we propose an algorithm of obtaining reachable points that uniformly fill the volume of the reachable set, and thus, result in a point cloud uniformly approximating a set even with a small number of points. To solve the task of finding each additional point is to solve the maximin optimal control problem. The design of the method allows considering reachable sets not only of two-dimensional systems but of multidimensional ones as well. The computational experiments conducted with the use of the proposed algorithm confirm the efficiency of the approach.

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Acknowledgements

This work is partly supported by Grant No. 15-07-03827 of the Russian Foundation for Basic Research.

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  1. Laboratory of Optimal Control, Matrosov Institute for System Dynamics and Control Theory SB RAS, 134 Lermontov Str., Irkutsk, Russia, 664033

    Alexandr Yu. Gornov, Evgeniya A. Finkelstein & Tatiana S. Zarodnyuk

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  1. Alexandr Yu. Gornov
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  2. Evgeniya A. Finkelstein
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  3. Tatiana S. Zarodnyuk
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Correspondence to Evgeniya A. Finkelstein.

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Gornov, A.Y., Finkelstein, E.A. & Zarodnyuk, T.S. Algorithm of uniform filling of nonlinear dynamic system reachable set based on maximin problem solution. Optim Lett 13, 633–643 (2019). https://doi.org/10.1007/s11590-018-1368-1

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