Quantitative Implementation Strategies for Safety Controllers

TL;DR

This paper introduces a unified framework for implementing safety controllers in nonlinear systems, optimizing long-term performance through a systematic selection of discount factors in game-based synthesis.

Contribution

It unifies existing control implementation strategies using a single discount factor approach and provides a method to systematically select optimal implementation parameters.

Findings

The choice of discount factor significantly affects long-term costs.

Optimal discount factors can reduce costs by up to 50% compared to previous heuristics.

Experimental results validate the effectiveness of the proposed approach.

Abstract

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.