code: public void exitApplication() {
          if (currentController != null) {
              currentController.hide(Actions.sequence(hidingActionProvider.provideAction(currentController, null),
                      Actions.run(CommonActionRunnables.getApplicationClosingRunnable())));
          } else {
              Gdx.app.exit();
          }
      }
docs: Allows to smoothly close the application by hiding the current screen and calling
  {@link com.badlogic.gdx.Application#exit()}.