  In this article, a notion of viscosity solutions is introduced for first
order path-dependent Hamilton-Jacobi-Bellman (HJB) equations associated with
optimal control problems for path-dependent differential equations. We identify
the value functional of the optimal control problems as a unique viscosity
solution to the associated HJB equations. We also show that our notion of
viscosity solutions is consistent with the corresponding notion of classical
solutions, and satisfies a stability property.
