About the attainability set of control system without assumption of compactness of geometrical restrictions on admissible controls

We investigate the conditions under which the control system $\dot x=f(t,x,u)$, $u\in U (t,x)$ together with closure of set of shifts (concerning time $t$) of control system possesses property of uniform local or uniform global attainability on the given time interval. We do not suppose that function $(t,x)\to U(t,x)$, setting geometrical restrictions on admissible controls $u(t,x)\in U(t,x)$, has convex compact images and we do not suppose that differential inclusion corresponding to control system has convex images.