1st response would be to avoid ghettoization, which as has been amply demonstrated is a huge drain on the social fabric for everyone
(there could perhaps be was that owners could be compensated but also not allowed to gouge)
How would you avoid ghettoization? Why wouldn't your rent controls just centralize poverty in the areas subject to those controls just as they are now? How would your idea differ from, say, the existing federal Section 8 program, which provides government subsidized rents based on the renter's income to private owners, where Section 8 homes already tend to be grouped together in ghettos?