Consider a simplified problem with two real variables $x_1$ and $x_2$, for which I I want to minimize
$x_1^2 +x_2^2$
under the following quadratic constraints:
$ d_1^2 \leq (x_1+x_2)^2 \leq d_2^2$
Is there any way to make this problem convex? For instance by adding a dummy variable as is done in Convex Programming Approach to Powered Descent Guidance for Mars Landing?
No, it is not possible in your case. Closest you can do is to realize that your case can be represented as the union of two polytopes (draw the set!), and thus it is MILP-representable.