On the continuity properties of the attainable sets of control systems with integral constraints on control Original Research Article

In the paper the attainable sets of the control systems with integral constraints on control are studied. It is assumed that the system is nonlinear with respect to the phase state vector and linear with respect to the control vector. The admissible control functions are chosen in Lp from the ball centered at the origin with given radius. It is proved that the attainable sets of the system are continuous with respect to p.