Reference Robust control for dynamical systems with non-gaussian noise via formal abstractions [badings_robust_2023]

@article{badings_robust_2023,
 abstract = {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.},
 author = {Badings, Thom and Romao, Licio and Abate, Alessandro and Parker, David and Poonawala, Hasan A. and Stoelinga, Marielle and Jansen, Nils},
 date = {2023-01-21},
 doi = {10.1613/jair.1.14253},
 file = {Full Text PDF:/home/eigil/Zotero/storage/4KYNP6D2/Badings et al. - 2023 - Robust Control for Dynamical Systems with Non-Gaus.pdf:application/pdf},
 issn = {1076-9757},
 journaltitle = {Journal of Artificial Intelligence Research},
 keywords = {markov decision processes, probabilistic reasoning, uncertainty},
 langid = {english},
 pages = {341--391},
 rights = {Copyright (c) 2023 Journal of Artificial Intelligence Research},
 title = {Robust Control for Dynamical Systems with Non-Gaussian Noise via Formal Abstractions},
 url = {https://jair.org/index.php/jair/article/view/14253},
 urldate = {2024-03-06},
 volume = {76}
}