  We propose an extension of the formalism developed by Stelle-West and
Grignani-Nardelli to the case of FDAs. We first consider the case of FDAs
carrying one $p$-form extension and no non-trivial cohomology. We show that it
is possible to define large gauge transformations as a direct extension of the
large transformations induced by their Lie subalgebras and study the resulting
non-linear realizations. Furthermore, we extend the results to the case FDAs
with non-trivial cohomology by introducing large gauge transformations that
carry the information about the FDA cocycle structure constants. We consider
two examples of this type of gauge algebra, namely, FDA extensions of the
bosonic Poincar\'{e} and Maxwell algebras, write down their dual $L_{\infty}$
algebras and study their non-linear realizations and possible invariant action
principles.
