...snif et m.... encore raté!

Thanks Alain, I've seen this info but, unlike in the shema of my first post, the High end is "open" (not connected) and I thought this would be okay this way.

Okay then, so how should I control the voltage regulator if not with my DS1804?

The AD7376 is another option, yes.

And yes, I've tried to control the LM317 with R+Tr already but you fully loose in ouput voltage precision.

Is there a other way to do?