Data-Driven Stability Certificate of Interconnected Homogeneous Networks via ISS Properties

This letter is concerned with a compositional data-driven approach for stability certificate of interconnected homogeneous networks with (partially) unknown dynamics while providing 100% correctness guarantees (as opposed to probabilistic confidence). The proposed framework enjoys input-to-state stability (ISS) properties of subsystems described by ISS Lyapunov functions. In our data-driven scheme, we first reformulate the corresponding conditions of ISS Lyapunov functions as a robust optimization program (ROP). Due to appearing unknown dynamics of subsystems in the constraint of ROP, we propose a scenario optimization program (SOP) by collecting data from trajectories of each unknown subsystem. We solve SOP and construct an ISS Lyapunov function for each subsystem with unknown dynamics. We accordingly leverage a compositional technique based on max -type small-gain reasoning and construct a Lyapunov function for an unknown interconnected network based on ISS Lyapunov functions of individual subsystems. We demonstrate the efficacy of our data-driven approach over a room temperature network containing 1000 rooms with unknown dynamics. Given collected data from each unknown room, we verify that the unknown interconnected network is globally asymptotically stable (GAS) with 100% correctness guarantee.