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

  • Alexandr Yu. Gornov
  • Evgeniya A. FinkelsteinEmail author
  • Tatiana S. Zarodnyuk
Original Paper


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.


Reachable set Optimal control Nonlinear dynamic system 



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


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratory of Optimal ControlMatrosov Institute for System Dynamics and Control Theory SB RASIrkutskRussia

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