  We consider the symbolic controller synthesis approach to enforce safety
specifications on perturbed, nonlinear control systems. In general, in each
state of the system several control values might be applicable to enforce the
safety requirement and in the implementation one has the burden of picking a
particular control value out of possibly many. We present a class of
implementation strategies to obtain a controller with certain performance
guarantees. This class includes two existing implementation strategies from the
literature, based on discounted payoff and mean-payoff games. We unify both
approaches by using games characterized by a single discount factor determining
the implementation. We evaluate different implementations from our class
experimentally on two case studies. We show that the choice of the discount
factor has a significant influence on the average long-term costs, and the best
performance guarantee for the symbolic model does not result in the best
implementation. Comparing the optimal choice of the discount factor here with
the previously proposed values, the costs differ by a factor of up to 50. Our
approach therefore yields a method to choose systematically a good
implementation for safety controllers with quantitative objectives.
