Data-Driven Safety Certificates of Infinite Networks with Unknown Models and Interconnection Topologies

Infinite networks are complex interconnected systems comprising a countably infinite number of subsystems, where counting them precisely poses a significant challenge due to the seemingly endless interconnected nature of the network (e.g., counting vehicles on the road). In such scenarios, the presence of infinitely many subsystems within the network renders the existing analysis frameworks tailored for finite networks inapplicable to infinite ones. This paper is concerned with offering a data-driven approach, within a compositional framework, for the safety certification of infinite networks with both unknown mathematical models and interconnection topologies. Given the immense computational complexity stemming from the extensive dimension of infinite networks, our approach capitalizes on the joint dissipativity-type properties of subsystems, characterized by storage certificates. We introduce innovative compositional data-driven conditions to construct a barrier certificate for the infinite network leveraging storage certificates of its unknown subsystems derived from data, while offering correctness guarantees across the network safety. We demonstrate that our compositional data-driven reasoning eliminates the requirement for checking the traditional dissipativity condition, which typically mandates precise knowledge of the interconnection topology. In addition, while existing data-driven literature demonstrates an exponential trend in sample complexity with respect to network size, we showcase that our compositional strategy notably reduces it to a linear scale in terms of the number of subsystems. We illustrate our data-driven results on two physical infinite networks with unknown models and interconnection topologies.