We descibe a dg-equivalence of dg-categories between Block's
$\mathcal{P}_{\A}$, corresponding to the de Rham dga $\A$ of a compact manifold
M and the dg-category of $\infty$-local systems on M. We understand this as a
generalization of the Riemann-Hilbert correspondence to $\Z$-graded connections
(superconnections in some formulations). An $\infty$-local system is an
$(\infty,1)$ functor between the $(\infty,1)$-categories ${\pi}_{\infty}M$ and
the linear simplicial nerve of the dg-category of cochain complexes.