DETROIT (AP) — Federal and state officials have approved a fix for 38,000 Volkswagen, Audi and Porsche sport utility vehicles with diesel engines that were cheating on emissions tests.

The U.S. Environmental Protection Agency and the California Air Resources Board approved the fix for 3-liter diesel engines in 2013-2016 models of the Volkswagen Touareg and Porsche Cayenne and the 2015 Audi Q7.

The vehicles have software that turns on emissions controls during testing but turns them off in everyday driving. German automaker Volkswagen AG will update the software in all of the vehicles and modify hardware in some of them. Owners also will receive compensation of up to $16,114.

Once the repairs are complete, Volkswagen will have repaired or bought back most of the 550,000 U.S. diesels involved in the two-year-old scandal.