On the approximation of the set of trajectories of control system described by a Volterra integral equation

Abstract

In this paper, the set of trajectories of the control system described by a nonlinear Volterra integral equation is studied. It is assumed that the set of admissible control functions is the closed ball of the space L-p, p > 1, with radius mu and centered at the origin. It is shown that the sections of the set of trajectories can be approximated by the sections of trajectories, generated by the mixed constrained and Lipschitz continuous control functions, the Lipschitz constant of which is bounded.