Compositional Safety Verification of Infinite Networks: A Data-Driven Approach

This paper develops a compositional framework for formal safety verification of an interconnected network comprised of a countably infinite number of discrete-time nonlinear subsystems with unknown mathematical models. Our proposed scheme involved subdividing the infinite network problem into individual subsystems, wherein the safety concept is modelled through a robust optimization program (ROP) via a notion of local-barrier certificates (L-BC). To address the difficulties associated with solving the ROP directly, primarily due to the absence of a mathematical model, we gather finite data from subsystem trajectories and leverage them to provide a scenario optimization program (SOP). We proceed with solving the resulted SOP and construct a local-barrier certificate for each unknown subsystem with a guarantee of correctness. Finally, in accordance with some small-gain conditions, we construct a global-barrier certificate (G-BC) derived from individual local certificates of subsystems, thus guaranteeing the safety of the infinite network within infinite time horizons. The practicality of our compositional findings becomes evident through a vehicle platooning scenario, characterized by a countably infinite number of vehicles with a single leader and an unlimited number of followers.