On the semicontinuity properties of the attainable sets of control systems with controls in

Abstract

In this article the properties of attainable sets of control systems with integral constraints on control are studied. The admissible control functions are chosen from the ball centered at the origin and of radius $mu_0$ in $L_p$, p > 1. It is proved that the attainable sets of the system at the fixed instant of time are left side lower semicontinuous and right side upper semicontinuous with respect to p.

In this article the properties of attainable sets of control systems with integral constraints on control are studied. The admissible control functions are chosen from the ball centered at the origin and of radius $mu_0$ in $L_p$, p > 1. It is proved that the attainable sets of the system at the fixed instant of time are left side lower semicontinuous and right side upper semicontinuous with respect to p.