Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation

Abstract

In this paper the control system with limited control resources is studied, where the behavior of the system is described by a nonlinear Volterra integral equation. The admissible control functions are chosen from the closed ball centered at the origin with radius A mu in L (p) (p > 1). It is proved that the set of trajectories generated by all admissible control functions is Lipschitz continuous with respect to A mu for each fixed p, and is continuous with respect to p for each fixed A mu. An upper estimate for the diameter of the set of trajectories is given.