Data-Driven Safety Certificates of Infinite Networks with Unknown Models and Interconnection Topologies
It addresses the safety verification problem for infinite networks, which existing finite-network methods cannot handle, but the results are incremental as they extend known dissipativity-based methods to a new setting.
This paper proposes a data-driven compositional framework for safety certification of infinite networks with unknown models and interconnection topologies. The approach uses storage certificates from subsystems to construct barrier certificates, eliminating the need for precise topology knowledge, and is demonstrated on two physical infinite networks.
Infinite networks are complex interconnected systems comprising a countably infinite number of subsystems, for which no fixed upper bound on the number of participating subsystems is specified a priori since it may vary over time as agents join or leave (e.g., vehicles in traffic). 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 unknown 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 for 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. We illustrate our data-driven results on two physical infinite networks with unknown models and interconnection topologies.