Construction of reachable sets of controlled systems with second order of accuracy with respect to time step
A.A. Ershov1,2
1Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
2Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg, Russia
Keywords: modified Euler method, second-order Runge-Kutta method, control system, reachable set, switching of control
Abstract
The paper investigates the pixel method for constructing reachable sets of a dynamic controlled system. Sufficient conditions for a control system have been obtained under which the explicit second order Runge-Kutta method (a modified Euler method) provides the second order of accuracy with respect to a time step in constructing reachable sets, even if discontinuous functions are in the class of admissible controls.
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