Hadi DAYEKH

Cyber-physical systems, which combine physical processes with computational elements, often exhibit hybrid dynamics, with interacting continuous and discrete behaviors. Such hybrid dynamics arise in numerous applications, from robotics to biological systems.

Identifying these systems from data is crucial for modeling, prediction and control; yet, it remains a challenging task due to the complexity of capturing both the continuous and discrete components from unlabeled data. Most hybrid system identification methods rely on passive learning, thus considering a fixed dataset without interacting with the system-under-learning. Active learning and counterexample-guided improvement of learned hybrid systems remain less explored. This thesis presents two approaches—a passive and an active method—for the learning of state-dependent switched nonlinear systems with continuous state variables. Both methods utilize segmentation to detect switching in observed trajectories. The passive approach involves solving an optimization problem over a fixed dataset to identify the continuous dynamics and mode regions, assuming a known number of modes. As the passive method is inherently limited by the completeness and quality of the initial dataset. The active approach incrementally learns the dynamics and mode information without prior assumptions about the number of modes. By leveraging equivalence queries, discrepancies between the learned model and the true system are identified, generating counterexamples that refine the model. We also provide a discussion on incremental learning of mode regions in the state space to better adapt the active learning approach. Both approaches are validated through a comprehensive set of experiments and a case study on electrical circuits, including benchmark systems like the Lorenz attractor and DC-DC converters. Results demonstrate the superiority of the active approach in achieving higher accuracy with reduced data requirements, while the passive method provides a baseline for well-defined datasets.