  In this article, we present a general methodology for control problems driven
by the Brownian motion filtration including non-Markovian and
non-semimartingale state processes controlled by mutually singular measures.
The main result of this paper is the development of a concrete pathwise method
for characterizing and computing near-optimal controls for abstract controlled
Wiener functionals. The theory does not require ad hoc functional
differentiability assumptions on the value process and elipticity conditions on
the diffusion components. The analysis is pathwise over suitable finite
dimensional spaces and it is based on the weak differential structure
introduced by Le\~ao, Ohashi and Simas jointly with measurable selection
arguments. The theory is applied to stochastic control problems based on
path-dependent SDEs where both drift and possibly degenerated diffusion
components are controlled. Optimal control of drifts for path-dependent SDEs
driven by fractional Brownian motion is also discussed. We finally provide an
application in the context of financial mathematics. Namely, we construct
near-optimal controls in a non-Markovian portfolio optimization problem.
