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We consider abstraction-based design of output-feedback controllers fordynamical systems with a finite set of inputs and outputs againstspecifications in linear-time temporal logic. The usual procedure forabstraction-based controller design (ABCD) first constructs a finite-stateabstraction of the underlying dynamical system, and second, uses reactivesynthesis techniques to compute an abstract state-feedback controller on theabstraction. In this context, our contribution is two-fold: (I) we define asuitable relation between the original system and its abstraction whichcharacterizes the soundness and completeness conditions for an abstractstate-feedback controller to be refined to a concrete output-feedbackcontroller for the original system, and (II) we provide an algorithm to computea sound finite-state abstraction fulfilling this relation.  Our relation generalizes feedback-refinement relations from ABCD withstate-feedback. Our algorithm for constructing sound finite-state abstractionsis inspired by the simultaneous reachability and bisimulation minimizationalgorithm of Lee and Yannakakis. We lift their idea to the computation of anobservation-equivalent system and show how sound abstractions can be obtainedby stopping this algorithm at any point. Additionally, our new algorithmproduces a realization of the topological closure of the input/output behaviorof the original system if it is finite-state realizable.

On Abstraction-Based Controller Design With Output Feedback