Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractions

Thom Badings, Licio Romao, Alessandro Abate, David Parker, Hasan A. Poonawala, Marielle Stoelinga, Nils Jansen

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying distributions are known and/or Gaussian. In practice, however, these assumptions may be unrealistic and can lead to poor approximations of the true noise distribution. We present a novel controller synthesis method that does not rely on any explicit representation of the noise distributions. In particular, we address the problem of computing a controller that provides probabilistic guarantees on safely reaching a target, while also avoiding unsafe regions of the state space. First, we abstract the continuous control system into a finite-state model that captures noise by probabilistic transitions between discrete states. As a key contribution, we adapt tools from the scenario approach to compute probably approximately correct (PAC) bounds on these transition probabilities, based on a finite number of samples of the noise. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP). This iMDP is, with a user-specified confidence probability, robust against uncertainty in the transition probabilities, and the tightness of the probability intervals can be controlled through the number of samples. We use state-of-the-art verification techniques to provide guarantees on the iMDP and compute a controller for which these guarantees carry over to the original control system. In addition, we develop a tailored computational scheme that reduces the complexity of the synthesis of these guarantees on the iMDP. Benchmarks on realistic control systems show the practical applicability of our method, even when the iMDP has hundreds of millions of transitions.

Original languageEnglish
Pages (from-to)341-391
Number of pages51
JournalJournal of Artificial Intelligence Research
StatePublished - 2023

Bibliographical note

Funding Information:
This work was partially funded by the NWO grant NWA.1160.18.238 (PrimaVera), the 2022 JPMorgan Chase Faculty Research Award “Learning and Reasoning in Repeated Games with Partial Information”, the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101008233, the ERC Consolidator Grant 864075 (CAESAR), the EPSRC IAA Award EP/X525777/1, and the ERC Advanced Grant 834115 (FUN2MODEL).

Publisher Copyright:
© 2023 AI Access Foundation. All rights reserved.

ASJC Scopus subject areas

  • Artificial Intelligence


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