Data-Driven Identification of Models for Discrete and Hybrid Systems

In this thesis, we develop data-driven methods for learning interpretable models of discrete and hybrid Cyber-Physical Systems (CPS). Manual modeling of complex CPS is often infeasible and prone to errors, making automated approaches essential for system understanding, testing, and optimization. This work has four contributions in data-driven model identification for CPS: first, analyzing the applicability of classical finite state machine learning to CPS, second, examining the performance of decision trees for modeling temporal behavior, third, developing methods for learning hybrid automata, and fourth, comparing the proposed approaches on qualitative and quantitative criteria. Three modeling strategies are presented spanning from discrete to hybrid models. First, the work extends classical automata learning with automata forests to improve robustness under data uncertainty while maintaining interpretability. Second, decision tree learning is specifically extended for CPS. The decision tree model handles nondeterministic behavior, establishing theoretical connections to deterministic finite automata and revealing fundamental limitations of finite-horizon model learning. Third, the work proposes two novel algorithms for hybrid automata learning that integrate discrete and continuous dynamics through symbolic regression. These algorithms enable efficient learning of hybrid systems and leverage system dynamics to identify transition points between modes. The proposed methods are evaluated on a diverse set of benchmark and real-world systems, demonstrating their effectiveness in capturing complex behaviors while remaining interpretable. We assess and compare the performance of the approaches on qualitative criteria such as interpretability and robustness as well as quantitative metrics including accuracy and computational efficiency. The results show that the approaches form a progression of complementary methods, each addressing different aspects of CPS modeling and providing a solid base for CPS-driven applications. The contributions advance the state-of-the-art in CPS modeling by providing robust, interpretable solutions.