From Data to Global Asymptotic Stability of Unknown Large-Scale Networks with Provable Guarantees

Mahdieh Zaker, Amy Nejati, Abolfazl Lavaei

Abstract:

We offer a compositional data-driven scheme for synthesizing controllers that ensure global asymptotic stability (GAS) across large-scale interconnected networks, characterized by unknown mathematical models. In light of each network’s configuration composed of numerous subsystems with smaller dimensions, our proposed framework gathers data from each subsystem’s trajectory, enabling the design of local controllers that ensure input-to-state stability (ISS) properties over subsystems, signified by ISS Lyapunov functions. To
accomplish this, we require only a single input-state trajectory from each unknown subsystem up to a specified time horizon, fulfilling
certain rank conditions. Subsequently, under small-gain compositional reasoning, we leverage ISS Lyapunov functions derived from data to offer a control Lyapunov function (CLF) for the interconnected network, ensuring GAS certificate over the network. We demonstrate that while the computational complexity for designing a CLF increases polynomially with the network dimension using sum-of-squares (SOS) optimization, our compositional data-driven approach significantly mitigates it to linear with respect to the number of subsystems. We showcase the efficacy of our data-driven approach over a set of benchmarks, involving physical networks with diverse interconnection topologies.