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arXiv · 2508.15543

Data-Driven Abstraction and Synthesis for Stochastic Systems with Unknown Dynamics

Mahdi Nazeri·Thom Badings·Anne-Kathrin Schmuck·Sadegh Soudjani·Alessandro Abate
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Abstract

We study the automated abstraction-based synthesis of correct-by-construction control policies for stochastic dynamical systems with unknown dynamics. Our approach is to learn an abstraction from sampled data, which is represented in the form of a finite Markov decision process (MDP). In this paper, we present a data-driven technique for constructing finite-state interval MDP (IMDP) abstractions of stochastic systems with unknown nonlinear dynamics. As a distinguishing and novel feature, our technique only requires (1) noisy state-input-state observations and (2) an upper bound on the system's Lipschitz constant. Combined with standard model-checking techniques, our IMDP abstractions enable the synthesis of policies that satisfy probabilistic temporal properties (such as "reach-while-avoid") with a predefined confidence. Our experimental results show the effectiveness and robustness of our approach.

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Mahdi Nazeri, Thom Badings, Anne-Kathrin Schmuck, Sadegh Soudjani, Alessandro Abate. 2025-08-21. Data-Driven Abstraction and Synthesis for Stochastic Systems with Unknown Dynamics. https://arxiv.org/abs/2508.15543

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