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.

中文翻译：

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构造关于时间步长的二阶精度控制系统的可到达集合

摘要

本文研究了用于动态控制系统的可达集的像素方法。已经获得了控制系统的充分条件，在这种条件下，即使允许控制的类别包括不连续的，在构造可达集时，显式二阶Runge-Kutta方法（改进的Euler方法）相对于时间步长也可以提供二阶精度。职能。