  We develop a systematic multi-local expansion of the Polchinski-Wilson exact
renormalization group (ERG) equation. Integrating out explicitly the non local
interactions, we reduce the ERG equation obeyed by the full interaction
functional to a flow equation for a function, its local part. This is done
perturbatively around fixed points, but exactly to any given order in the local
part. It is thus controlled, at variance with projection methods, e.g.
derivative expansions or local potential approximations. Our method is
well-suited to problems such as the pinning of disordered elastic systems,
previously described via functional renormalization group (FRG) approach based
on a hard cutoff scheme. Since it involves arbitrary cutoff functions, we
explicitly verify universality to ${\cal O} (\epsilon =4-D)$, both of the T=0
FRG equation and of correlations. Extension to finite temperature $T$ yields
the finite size ($L$) susceptibility fluctuations characterizing mesoscopic
behaviour $\bar{(\Delta \chi)^2} \sim L^\theta/T$, where $\theta$ is the energy
exponent. Finally, we obtain the universal scaling function to ${\cal
O}(\epsilon^{1/3})$ which describes the ground state of a domain wall in a
random field confined by a field gradient, compare with exact results and
variational method. Explicit two loop exact RG equations are derived and the
application to the FRG problem is sketched.
