Zaker et al. stabilize infinite networks with data-driven controller design

A team of researchers led by Mahdieh Zaker has developed a direct data-driven approach to stabilize infinite networks composed of unknown linear time-invariant subsystems. The method requires only a single set of noise-corrupted input-state trajectories from each subsystem. By solving certain linear matrix inequalities, the algorithm locally constructs an exponential input-to-state stable (eISS) control Lyapunov function along with a stabilizing feedback controller for each subsystem. This local stability is then composed under a novel compositional small-gain condition designed for infinite-dimensional spaces, producing a global control Lyapunov function and a controller that guarantees uniform global exponential stability of the entire infinite network.

The approach was validated on a physical case study with unknown dynamics, demonstrating its practical applicability. The paper has been accepted at the 27th International Symposium on Mathematical Theory of Networks and Systems (MTNS) 2026. This work addresses a critical gap in control theory: stabilizing large-scale or infinite networks without needing a mathematical model, using only data. It has potential applications in power grids, communication networks, biological systems, and any large-scale distributed system where modeling is impractical and data is noisy.