A philosophical question about filtrations and information sets

Question

In continuous-time stochastic calculus when we face an optimal control problem how can we restrict our choices to be "pre" variables rather than "post". To be clear, suppose that we are in a discrete-time setup, and at time $n$ we want to decide the optimum choice for $ X_n$, observing the values of $Y$ up to time $n$ and $Z$ up to time $n-1$. So what we choose is in the sigma-algebra generated by $(Y_k,Z_{k-1})_{k=0}^{n} $. How such a restriction can be made in the continuous time? For example let say that there are two independent Weiner processes $Y_t$ and $Z_t$ and we are deciding on $dX$ at time $t$. However, we want to restrict this rule to be such that it can have $dY$ terms inside the optimal rule, but not $dZ$. In some sense, $X$ is measurable with respect to filtration generated by $Y$ but it cannot be measurable w.r.t $Z$. However, the latter conclusion is obviously not sufficient for my purpose. Indeed at $t$ I want to be able to make my rule dependent on $Z_t$ but not $Z_t + dZ_t$. What I want is the rigorous requirement of such a policy. I mean what is the information set that I need to make my $X$ measurable to?