From Data to Control: A Formal Compositional Framework for Large-Scale Interconnected Networks

Abstract: We introduce a compositional data-driven methodology with noisy data for designing fully-decentralized safety controllers applicable to large-scale interconnected networks, encompassing a vast number of subsystems with unknown mathematical models. Our compositional scheme leverages the interconnection topology and breaks down the network analysis into the examination of distinct subsystems. This is accompanied by utilizing a concept of control storage certificates (CSCs) to capture joint dissipativity-type properties among subsystems. These CSCs are instrumental in a compositional derivation of a control barrier certificate (CBC) specialized for the interconnected network, thereby ensuring its safety. In our data-driven scheme, we gather only a single noise-corrupted input-state trajectory from each unknown subsystem within a specified time frame. By fulfilling a specific rank condition, this process facilitates the construction of a CSC for each subsystem. Following this, by adhering to compositional dissipativity reasoning, we compose CSCs derived from noisy data and build a CBC for the unknown network, ensuring its safety over an infinite time horizon, while providing correctness guarantees. We demonstrate that our compositional data-driven approach significantly enhances the design of a CBC and its robust safety controller under noisy data across the interconnected network. This advancement is achieved by reducing the computational complexity from a polynomial growth in relation to network dimension, when using sum-of-squares (SOS) optimization, to a linear scale based on the number of subsystems. We apply our data-driven findings to a variety of benchmarks, involving physical networks with unknown models and diverse interconnection topologies.