Nobody really controls the crypto market because it is not owned by anyone. But manipulation in terms of price movements is a different story. Government agencies / institutions, banks, private entities, high-profile and influential individuals who have a lot of cryptocurrency in their pockets can easily manipulate prices according to their wishes simply by buying or selling large amounts of their ownership.
Whoever have a large capital investment and understand how the market flows can manipulate this type of investment, the mentality of weak holders always depend on the short term movements, that's why people who can shake the market with their holdings can move the price from what they wanted to happen, then panic sellers and weak investors followed allowing manipulators to gained more and play with their assets.