  Let $X$ be a compact, oriented, second countable pseudomanifold. We show that
$HH^\ast_\bullet(\widetilde N^\ast_\bullet(X;\mathbb{Q}))$, the Hochschild
cohomology of the blown-up intersection cochain complex of $X$, is well defined
and endowed with a Batalin-Vilkovisky algebra structure. Furthermore, we prove
that it is a topological invariant. More generally, we define the Hochschild
cohomology of a perverse differential graded algebra $A_\bullet$ and present a
natural Gerstenhaber algebra structure on it. This structure can be extended
into a Batalin-Vilkovisky algebra when $A_\bullet$ is a derived Poincar\'e
duality algebra.
