Approximation of sections of the set of trajectories for a control system with bounded control resources

A. Huseyin, N. Huseyin, Kh. Guseinov. Approximation of sections of the set of trajectories for a control system with bounded control resources. 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.