The typo3 cache can be deleted in an extbase controller the following way:
use TYPO3\CMS\Extbase\Object\ObjectManager;
class Something {
public function foo(){
$objectManager = new ObjectManager();
$clearCacheService = $objectManager->get('TYPO3\\CMS\\Install\\Service\\ClearCacheService');
$clearCacheService->clearAll();
}
}
I didn’t find out yet how to delete just one certain cache, i.e. only the Frontend Cache.