APPROXIMATION OF THE SECTIONS OF THE SET OF TRAJECTORIES OF THE CONTROL SYSTEM DESCRIBED BY A NONLINEAR VOLTERRA INTEGRAL EQUATION

Abstract

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 µ 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.