A Compositional Dissipativity Approach for Data-Driven Safety Verification of Large-Scale Dynamical Systems

Abolfazl Lavaei, Sadegh Soudjani, Emilio Frazzoli

Abstract: This work is concerned with a compositional data-driven approach for formal safety verification of large-scale continuous-time dynamical systems with unknown models. The proposed framework enjoys the interconnection matrix and joint dissipativity-type properties of subsystems, described by the notion of stochastic storage certificates. In the first part of the paper, we cast the required conditions for constructing storage certificates as a robust optimization program (ROP). Since the proposed ROP is not tractable due to the unknown model appearing in one of its constraints, we propose a scenario optimization program (SOP) corresponding to the original ROP by collecting finite numbers of data from trajectories of each subsystem. By establishing a probabilistic relation between the optimal value of SOP and that of ROP, we construct a storage certificate for each unknown subsystem based on the number of data and a required level of confidence. We accordingly propose a compositional technique based on dissipativity reasoning to construct stochastic barrier certificates of interconnected systems based on storage certificates of individual subsystems. By leveraging the acquired barrier certificate, we quantify a lower bound on the probability that an interconnected system never reaches a certain unsafe region in finite-time horizons with an a-priori guaranteed confidence. We also propose an auxiliary compositional approach without requiring any compositionality condition but at the cost of providing a potentially conservative safety guarantee. In the second part of the paper, we propose our approaches for deterministic continuous-time systems with unknown dynamics. We verify our results over an unknown room temperature network containing 100 rooms.