TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, vol.23, no.1, pp.116-127, 2017 (ESCI)
The approximation of the set of trajectories is studied for a control system described by the Urysohn integral equation. It is assumed that the system has limited control resources. The closed ball of the space L-p, p > 1, with radius r centered at the origin is chosen as the set of admissible control functions. The set of admissible control functions is replaced step by step by a set that consists of a finite number of control functions and generates a finite number of trajectories. It is proved that sections of the set of trajectories can be approximated by sections of a set consisting of a finite number of trajectories.