# On Abstraction-Based Controller Design With Output Feedback

arXiv: https://arxiv.org/abs/2002.02687 · HTML: https://mlsanity.com/paper/2002.02687/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2020.

## Built on by (most cited first, 3 of 3)

- [Shielded Reinforcement Learning for Hybrid Systems](https://mlsanity.com/paper/2308.14424/) (2023)
- [Data-driven abstractions via adaptive refinements and a Kantorovich metric [extended version]](https://mlsanity.com/paper/2303.17618/) (2023)
- [Neural Abstraction-Based Controller Synthesis and Deployment](https://mlsanity.com/paper/2307.03783/) (2023)

## Abstract (arXiv)

We consider abstraction-based design of output-feedback controllers for dynamical systems with a finite set of inputs and outputs against specifications in linear-time temporal logic. The usual procedure for abstraction-based controller design (ABCD) first constructs a finite-state abstraction of the underlying dynamical system, and second, uses reactive synthesis techniques to compute an abstract state-feedback controller on the abstraction. In this context, our contribution is two-fold: (I) we define a suitable relation between the original system and its abstraction which characterizes the soundness and completeness conditions for an abstract state-feedback controller to be refined to a concrete output-feedback controller for the original system, and (II) we provide an algorithm to compute a sound finite-state abstraction fulfilling this relation. Our relation generalizes feedback-refinement relations from ABCD with state-feedback. Our algorithm for constructing sound finite-state abstractions is inspired by the simultaneous reachability and bisimulation minimization algorithm of Lee and Yannakakis. We lift their idea to the computation of an observation-equivalent system and show how sound abstractions can be obtained by stopping this algorithm at any point. Additionally, our new algorithm produces a realization of the topological closure of the input/output behavior of the original system if it is finite-state realizable.