# Automata-based Controller Synthesis for Stochastic Systems: A Game Framework via Approximate Probabilistic Relations

arXiv: https://arxiv.org/abs/2104.11803 · HTML: https://mlsanity.com/paper/2104.11803/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2021.

## Built on by (most cited first, 1 of 1)

- [Transfer Learning for Control Systems via Neural Simulation Relations](https://mlsanity.com/paper/2412.01783/) (2024)

## Abstract (arXiv)

In this work, we propose an abstraction and refinement methodology for the controller synthesis of discrete-time stochastic systems to enforce complex logical properties expressed by deterministic finite automata (a.k.a. DFA). Our proposed scheme is based on a notion of so-called (ε,δ)-approximate probabilistic relations, allowing one to quantify the similarity between stochastic systems modeled by discrete-time stochastic games and their corresponding finite abstractions. Leveraging this type of relations, the lower bound for the probability of satisfying the desired specifications can be well ensured by refining controllers synthesized over abstract systems to the original games. Moreover, we propose an algorithmic procedure to construct such a relation for a particular class of nonlinear stochastic systems with slope restrictions on the nonlinearity. The proposed methods are demonstrated on a quadrotor example, and the results indicate that the desired lower bound for the probability of satisfaction is guaranteed.