To answer your question we need to build in a love lock ("aren’t these humans adorable") that builds a smarter love lock and hope the chain hold as AI scales up to the Singularity.

The more likely result is we lose control of the AI’s since the last 100x increase will occur too fast for us to deal with. Even if the generalised Moore’s doesn’t accelerate over the last 100x leap, we only have 10 years from 0.01x to 1x.