Correct-by-Construction Control for Stochastic and Uncertain Dynamical Models via Formal Abstractions

Thom Badings
(Radboud University)
Nils Jansen
(Radboud University)
Licio Romao
(University of Oxford)
Alessandro Abate
(University of Oxford)

Automated synthesis of correct-by-construction controllers for autonomous systems is crucial for their deployment in safety-critical scenarios. Such autonomous systems are naturally modeled as stochastic dynamical models. The general problem is to compute a controller that provably satisfies a given task, represented as a probabilistic temporal logic specification. However, factors such as stochastic uncertainty, imprecisely known parameters, and hybrid features make this problem challenging. We have developed an abstraction framework that can be used to solve this problem under various modeling assumptions. Our approach is based on a robust finite-state abstraction of the stochastic dynamical model in the form of a Markov decision process with intervals of probabilities (iMDP). We use state-of-the-art verification techniques to compute an optimal policy on the iMDP with guarantees for satisfying the given specification. We then show that, by construction, we can refine this policy into a feedback controller for which these guarantees carry over to the dynamical model. In this short paper, we survey our recent research in this area and highlight two challenges (related to scalability and dealing with nonlinear dynamics) that we aim to address with our ongoing research.

In Marie Farrell, Matt Luckcuck, Mario Gleirscher and Maike Schwammberger: Proceedings Fifth International Workshop on Formal Methods for Autonomous Systems (FMAS 2023), Leiden, The Netherlands, 15th and 16th of November 2023, Electronic Proceedings in Theoretical Computer Science 395, pp. 144–152.
Published: 15th November 2023.

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