Cup product on $A_\infty$-cohomology and deformations

We propose a simple method for constructing formal deformations of differential graded algebras in the category minimal $A_\infty$-algebras. The basis our approach is provided by Gerstenhaber algebra structure on $A_\infty$-cohomology, which we define terms brace operations. As an example, construct $A_\infty$-algebra from Weyl-Moyal $\ast$-product polynomial functions.