No one would control them, they'd be under whatever Avenger was leading the team at the moment...which was between Cap or Tony. And neither of them ever take the word 'no' too well, do they?
"The Sokovia Accords. Approved by 117 countries, it states that the Avengers shall no longer be a private organization. Instead, they'll operate under the supervision of a United Nations panel, only when and if that panel deems it necessary."
Ratified by 117 countries, the Accords place the Avengers under U.N. authority and provide a framework for the registration and monitoring of all Enhanced individuals."
The currently known regulations established by the Sokovia Accords include:
Any enhanced individuals who agree to sign must register with the United Nations and provide biometric data such as fingerprints and DNA samples.
Those with secret identities must reveal their legal names and true identities to the United Nations.
Those with innate powers must submit to a power analysis, which will categorize their threat level and determine potential health risks.
Those with innate powers must also wear tracking bracelets at all times.
Any enhanced individuals who sign are prohibited from taking action in any country other than their own unless they are first given clearance by either that country's government or by a United Nations subcommittee.
Governments are forbidden from deploying enhanced individuals outside of their own national borders unless those individuals are given clearance as described above. The same rule also applies to non-government organizations that operate on a global scale (including S.H.I.E.L.D. and the Avengers).
Any enhanced individuals who do not sign will not be allowed to take part in any police, military, or espionage activities, or to otherwise participate in any national or international conflict, even in their own country.
As a corollary, they will not be allowed to participate in any active missions undertaken by private or governmental law enforcement/military/intelligence organizations (such as S.H.I.E.L.D. and the Avengers).
Any enhanced individuals who use their powers to break the law (including those who take part in extralegal vigilante activities), or are otherwise deemed to be a threat to the safety of the general public, may be detained indefinitely without trial.
If an enhanced individual violates the Accords, or obstructs the actions of those enforcing the Accords, they may likewise be arrested and detained indefinitely without trial.[2]
The use of technology to bestow individuals with innate superhuman capabilities is strictly regulated, as is the use and distribution of highly advanced technology (such as Asgardian and Chitauri weaponry).
The creation of self-aware artificial intelligence is completely prohibited.
The Avengers will no longer be a private organization and will operate under the supervision of the United Nations.
For the purposes of the Accords, an "enhanced individual" is defined as any person, human or otherwise, with superhuman capabilities. This includes individuals whose powers are an innate function of their biology as well as individuals who utilize the highly advanced technology to grant themselves superhuman capabilities. However, individuals with advanced prostheses do not seem to be considered "enhanced", even if their prostheses give them capabilities beyond those of ordinary humans.
All members of the Avengers are subject to the same conditions as enhanced individuals, even if they are not enhanced themselves: Black Widow was required to sign so she could continue serving on the Avengers due to her previously being deemed a threat to world security by Nick Fury, and Hawkeye was incarcerated on the Raft after violating the Accords.