On the continuity properties of the attainable sets of control systems with integral constraints on control. (Q1427930)

The authors consider a control system whose behavior is described by a differential equation \[ \dot x=f(t,x(t))+B(t,x(t))u(t), \quad x(t_{0})\in X_{0}, \] with constraints \[ \int_{t_{0}}^{\theta}\| u(t)\| ^{p}\,dt\leq \mu_{o}^{p}, \quad \mu_{0}>0, 1<p<\infty, \] and prove that the attainable sets of the system are continuous with respect to \(p\)