No. That would defeat the object of it being 'smart'. The while punt is that it wakes you when you will get the most benefit. If you could control it, it would just be an 'alarm'
Again, the Band decides when to wake you up, which "could" be up to a 30 minute timeframe. It may determine the optimal time to wake you up is 15 minutes earlier. It is a window around the time you set for the alarm.