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In this paper, we consider the problem of controller design usingapproximately bisimilar abstractions with an emphasis on safety andreachability specifications. We propose abstraction-based approaches to solveboth classes of problems. We start by synthesizing a controller for anapproximately bisimilar abstraction. Then, using a concretization procedure, weobtain a controller for our initial system that is proved "correct by design".We provide guarantees of performance by giving estimates of the distance of thesynthesized controller to the maximal (i.e the most permissive) safetycontroller or to the time-optimal reachability controller. Finally, we use thepresented techniques combined with discrete approximately bisimilarabstractions of switched systems developed recently, for switching controllersynthesis.

Controller Synthesis for Safety and Reachability via Approximate Bisimulation