ABSTRACT
The paper investigates the pixel method for constructing reachable sets for a dynamic control system. Sufficient conditions for a control system have been obtained under which the explicit second order Runge–Kutta method (the modified Euler method) provides the second order of accuracy with respect to the time step when constructing reachable sets even if the class of admissible controls includes discontinuous functions.
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ACKNOWLEDGMENTS
The author thanks V.N. Ushakov for setting the problem and V.G. Pimenov for helpful discussions.
Funding
This work was supported by RFBR (project no. 18-01-00221) and by RF Ministry of Education and Science (Government Decree no. 211, contract no. 02.A03.21.0006).
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Ershov, A.A. Constructing Reachable Sets for Control Systems of Second Order of Accuracy with Respect to Time Step. Numer. Analys. Appl. 13, 306–320 (2020). https://doi.org/10.1134/S1995423920040023
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DOI: https://doi.org/10.1134/S1995423920040023