MATHEMATICAL MODELLING AND ANALYSIS, vol.20, no.4, pp.502-515, 2015 (SCI-Expanded)
Approximation of the sections of the set of trajectories of the control system described by a nonlinear Volterra integral equation is studied. The admissible control functions are chosen from the closed ball of the space L-p, p > 1, with radius mu and centered at the origin. The set of admissible control functions is replaced by the set of control functions, which includes a finite number of control functions and generates a finite number of trajectories. It is proved that the sections of the set of trajectories can be approximated by the sections of the set of trajectories, generated by a finite number of control functions.