conditional expectation related to an AR model

Question

Suppose we have an AR model like:

$\dot{h}(t)=ah(t)+w(t)$

where $a<0$, $w(t)\sim \mathcal{CN}(0,1)$. My question is how to evaluate the following conditional expectation:

$\mathbb{E}\big[h(t) \big| \{h(s):0\leq s<t\}\big]$.

Thanks.