# An Iterative Abstraction Algorithm for Reactive Correct-by-Construction Controller Synthesis

arXiv: https://arxiv.org/abs/1509.04125 · HTML: https://mlsanity.com/paper/1509.04125/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2015.

## Built on by (most cited first, 2 of 2)

- [ISAACS: Iterative Soft Adversarial Actor-Critic for Safety](https://mlsanity.com/paper/2212.03228/) (2022)
- [Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imagination](https://mlsanity.com/paper/2405.00846/) (2024)

## Abstract (arXiv)

In this paper, we consider the problem of synthesizing correct-by-construction controllers for discrete-time dynamical systems. A commonly adopted approach in the literature is to abstract the dynamical system into a Finite Transition System (FTS) and thus convert the problem into a two player game between the environment and the system on the FTS. The controller design problem can then be solved using synthesis tools for general linear temporal logic or generalized reactivity(1) specifications. In this article, we propose a new abstraction algorithm. Instead of generating a single FTS to represent the system, we generate two FTSs, which are under- and over-approximations of the original dynamical system. We further develop an iterative abstraction scheme by exploiting the concept of winning sets, i.e., the sets of states for which there exists a winning strategy for the system. Finally, the efficiency of the new abstraction algorithm is illustrated by numerical examples.