Quantitative Implementation Strategies for Safety Controllers
For practitioners designing safety controllers with quantitative performance objectives, this work provides a systematic method to choose implementation strategies that significantly improve long-term costs.
The paper addresses the problem of selecting control values from multiple safe options in symbolic controller synthesis for safety specifications. It proposes a class of implementation strategies unified by a discount factor, showing that the optimal choice can reduce average long-term costs by a factor of up to 50 compared to previous methods.
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.