  $L_{\infty}$ algebras have been recently studied as algebraic frameworks in
the formulation of gauge theories in which the gauge symmetries and the
dynamics of the interacting theories are contained in a set of products acting
on a graded vector space. On the other hand, FDAs are differential algebras
that generalize Lie algebras by including higher-degree differential forms on
their differential equations. In this article, we review the dual relation
between FDAs and $L_{\infty}$ algebras. We study the formulation of standard
Chern--Simons theories in terms of $L_{\infty}$ algebras and extend the results
to FDA-based gauge theories. We focus on two cases, namely a flat (or
zero-curvature) theory and a generalized Chern--Simons theory, both including
high-degree differential forms as fundamental fields.
