Suppose that we have two differential inclusions $$dY^1(t)\in b_1(Y^1,t)$$ with $Y^1(0)\in Y_0^1$ and $$dY^2(t)\in b_2(Y^2,t)$$ with $Y^2(0)\in Y_0^2$. Can we then control $d(Y^1(t),Y^2(t))$ by the distance of $b_1$ and $b_2$ and the initial conditions? The distance here would be some appropriate set distance such as Kuratowski or Hausdorff distance or some other distance?