caa a22 4500 606217037 CHVBK 20210128101106.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s10598-014-9259-5 doi (NATIONALLICENCE)springer-10.1007/s10598-014-9259-5 Vinnikov E. Lomonosov Moscow State University, Faculty of Computation Mathematics and Cybernetics, Moscow, Russia aut Construction of Attainable Sets and Integral Funnels of Nonlinear Controlled Systems in the Matlab Environment [Elektronische Daten] [E. Vinnikov] Attainable sets play an important role in investigating the behavior of controlled systems. The pixel method [1,2] is a universal numerical method for the construction of attainable sets of nonlinear controlled system. In the first part of the article, we describe the pixel method that requires partition of the phase space into n-dimensional cubes and time discretization using Euler and Runge-Kutta methods of second order approximation. This method enables us to construct attainability and controllability sets as well as integral funnels for nonlinear controlled systems described by a system of differential equations with controlled parameters, both with and without phase constraints. For attainable sets constructed by the pixel method, we have obtained bounds on the Hausdorff distance between the exact attainable set and its discrete approximation. These bounds lead to a relationship between the partition parameters in time and phase coordinates. In the second part of the article, we present a description of the program PixelSet developed in the Matlab environment for the construction of attainable sets and integral funnels of two- and three-dimensional nonlinear controlled systems by the pixel method. We present examples of the construction of attainable sets of some two- and three-dimensional controlled systems. Springer Science+Business Media New York, 2014 nonlinear control systems nationallicence phase constraints nationallicence attainable set nationallicence Computational Mathematics and Modeling Springer US; http://www.springer-ny.com 26/1(2015-01-01), 107-119 1046-283X 26:1<107 2015 26 10598 https://doi.org/10.1007/s10598-014-9259-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10598-014-9259-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Vinnikov E. Lomonosov Moscow State University, Faculty of Computation Mathematics and Cybernetics, Moscow, Russia aut NATIONALLICENCE 773 0- Computational Mathematics and Modeling Springer US; http://www.springer-ny.com 26/1(2015-01-01), 107-119 1046-283X 26:1<107 2015 26 10598