Is there any reference for gluing in the context of Morse homology on Hilbert manifolds?

Gluing is pretty standard in Morse homology for finite-dimensional manifolds. Unfortunately, in the infinite-dimensional case the sources I know avoid gluing. For proving that the Morse boundary operator squares to zero Abbondandolo-Majer use either an argument involving cellular filtrations or the graph transform method.

Unfortunately, in the context I want to consider, namely proving that some Morse-like theory is isomorphic to singular homology, both of these approaches do not work. (The latter approach works for showing that my Morse-like theory has a boundary operator that squares to zero, though.)

Reading through the finite-dimensional case ("Morse homology" of Schwarz) I realized that there are a lot of arguments which make it difficult to generalize the gluing procedure to cases where the target is not locally compact. For instance, in a lot of indirect arguments, the Rellich compact embedding theorem is used, which fails if the target is infinite-dimensional.

So, is there any instance where gluing in an infinite-dimensional context ist proved? Are there certain obstacles not yet overcome?

Is there any reference for gluing in the context of Morse homology on Hilbert manifolds?

Gluing is pretty standard in Morse homology for finite-dimensional manifolds. Unfortunately, in the infinite-dimensional case the sources I know avoid gluing. For proving that the Morse boundary operator squares to zero Abbondandolo-Majer use either an argument involving cellular filtrations or the graph transform method.

Unfortunately, in the context I want to consider, namely proving that some Morse-like theory is isomorphic to singular homology, both of these approaches do not work. (The latter approach works for showing that my Morse-like theory has a boundary operator that squares to zero, though.)

Reading through the finite-dimensional case ("Morse homology" of Schwarz) I realized that there are a lot of arguments which make it difficult to generalize the gluing procedure to cases where the target is not locally compact. For instance, in a lot of indirect arguments, the Rellich compact embedding theorem is used, which fails if the target is infinite-dimensional.

So, is there any instance where gluing in an infinite-dimensional context is proved? Are there certain obstacles not yet overcome?