Renting to illegal immigrants , rent control

This might be a sensitive topic. I have a unit in the city of Los Angeles, echo park area.   tenants moved into the building with the prior owner and at the time that they moved in ( 2011), it was just mother and father with 3 minor children. , the kids are now adults and no one has moved out. So there are 5 adults and they all live in a 1 bedroom unit. I don’t want to kick them out because they are good, law abiding , rent paying tenants. However, their rent is well below market at $1,000 a month. I want to negotiate with them to sign a new lease with a higher rent( $1500). However, the unit is a rent controlled building built in 1940s. What would u do?  is it legal to request a rent controlled tenant to pay higher ? Would I be harassing them because they are illegal immigrants?