The international free market in currency establishes the value of the dollar. No one controls it.
"The Congress shall have Power
... To coin Money, regulate the Value thereof, and of foreign Coin"
Constitution of the United States
Congress has unwisely chosen to ignore this power. The "international free market" is manipulated by the IMF and the Federal Reserve Board to such a degree that the freedom of the market is a myth, except within narrow bounds.
I don't believe that over the long run free markets can be manipulated. The Hunt brothers learned this the hard way when they tried to corner the market in silver.