Generalized sigma model with dynamical antisymplectic potential and non-Abelian de Rham's differential

For topological sigma models, we propose that their local Lagrangian density is allowed to depend non-linearly on the de Rham's “velocities” DZA. Then, by differentiating the Lagrangian density with respect to the latter de Rham's “velocities”, we define a “dynamical” anti-symplectic potential, in terms of which a “dynamical” anti-symplectic metric is defined, as well. We define the local and the functional antibracket via the dynamical anti-symplectic metric. Finally, we show that the generalized action of the sigma model satisfies the functional master equation, as required.