The entropy of a system.- The minimum entropy $$\mathcal_\infty$$ control problem.- The minimum entropy $$\mathcal_\infty$$ distance problem.- Relations to combined $$\mathcal_\infty$$ /LQG control.- Relations to risk-sensitive LQG control.- The normalized $$\mathcal_\infty$$ control problem.- $$\mathcal_\infty$$ -characteristic values.- LQG and $$\mathcal_\infty$$ monotonicity.