From Data to Sliding Mode Control of Uncertain Large-Scale Networks with Unknown Dynamics

Large-scale interconnected networks, composed of multiple low-dimensional subsystems, serve as a crucial framework for modeling a wide range of real-world applications. Despite offering computational scalability, the inherent interdependence among subsystems poses significant challenges to the effective control of such networks. This complexity is further exacerbated in the presence of external perturbations and when the dynamics of individual subsystems, and accordingly the overall network, are unknown-scenarios frequently encountered in modern practical applications. In this paper, we develop a compositional data-driven approach to ensure the global asymptotic stability (GAS) of large-scale nonlinear networks with unknown mathematical models, subjected to external perturbations. To achieve this, we first gather two sets of data from each unknown nominal subsystem without perturbation, which we refer to as two input-state trajectories. The collected data from each subsystem is then utilized to design an input-to-state stable (ISS) Lyapunov function and its corresponding controller for each nominal subsystem, rendering them ISS. To cancel the effect of external perturbations on the dynamic of each subsystem, and accordingly the whole network, we then design a local integral sliding mode (ISM) controller for each subsystem using the collected data. Under a small-gain compositional condition, we employ data-driven ISS Lyapunov functions designed for subsystems and construct a control Lyapunov function for the network, rendering the assurance of GAS property over the nominal network. We then extend this compositional result to network perturbed models, demonstrating that the synthesized ISM controllers ensure the GAS property even in the presence of perturbations.