What happens to consumer and producer surplus after a rent control is established? Do they increase or decrease?

The history of rent controls in the United States and in other industrialized Western countries suggests that such controls lead to higher overall housing costs and to reduced availability of rental housing units. The reason, as has been determined in studies over the years, is that rental housing in noncontrolled complexes invariably rises as occupants in controlled units enjoy stable, lower rental fees. Occupants of rent-controlled units tend to remain in place because of the lower rents. Even in those apartment and housing complexes that enjoy government-imposed rent controls, the quality of consumer life tends to dissipate over time as owners find it less and less attractive to invest in housing units whose potential for return on investment is more and more questionable. In other words, where is the incentive to maintain and improve housing whose revenue is controlled by the government?
An obvious alternative to the consequences of rent control is the implementation of universal government controls on housing costs. This would eliminate the possibility of the owners of noncontrolled housing from benefiting from the shortage of rent-controlled units that invariably develops over time. That level of government control would also apply to the problem of capital flight from cities or states with higher tax rates—rates that encourage wealthier members of society to move to lower-tax-rate venues. The only "fix" to that problem is the imposition of "capital controls," which prohibits the freedom of movement of people and their money. If most Americans decide that they wish to live in a country in which the government wields that much control over the economy, that is fine. Otherwise, the disparities will continue to exist.
The history of rent controls, as discussed in the studies the links to which are provided below, points toward the emergence over time of housing shortages. The costs associated with building and maintaining dwellings are subject to frequent and dramatic changes, dependent as they are on a host of ancillary costs—such as plumbing, construction and electrical supplies, and the cost of labor—to say nothing of variations in utility costs that would have to be passed on to the consumer. Rent controls are great for those fortunate enough to occupy such dwellings at the time controls are imposed. They are not so good for those who do not occupy such units and are unlikely to able to until rent-controlled units become available or more are built, the latter of which is improbable. And the alternative of government-financed and -operated housing units is not very impressive, as those who have toured or occupied apartment or housing units in areas like Coney Island and Brooklyn and on military installations can attest.
https://www.bloomberg.com/tosv2.html?vid=&uuid=dce31060-6c2c-11e9-a3c7-33984bee415b&url=L29waW5pb24vYXJ0aWNsZXMvMjAxOC0wMS0xOC95dXAtcmVudC1jb250cm9sLWRvZXMtbW9yZS1oYXJtLXRoYW4tZ29vZA==

https://www.brookings.edu/research/what-does-economic-evidence-tell-us-about-the-effects-of-rent-control/

https://www.econlib.org/library/Enc/RentControl.html