Federated Learning-Based Offset-Free Distributed Control of Nonlinear Networked Systems With Application to IIoT

Preserving data privacy in data-driven modeling for the Industrial Internet of Things (IIoT) has become critically important due to the susceptibility of communication data from numerous devices to cyber-attacks. Given its multi-subsystem integration, nonlinear interactions, and networking characteristics, IIoT can be modeled as nonlinear networked systems (NNSs). This paper presents a federated learning-based offset-free distributed control (FL-OFDC) method for NNSs with multiple subsystems to preserve data privacy and achieve offset-free control, with potential applications to IIoT. First, a novel FL algorithm with personalized optimization (FLPO) is proposed to simultaneously obtain global and local models using a simple algorithm framework, which can preserve data privacy and address the heterogeneity issue among subsystems. Subsequently, a novel information-theoretic bound for the generalization error of the FLPO algorithm with iteration properties is constructed using individual sample mutual information. Next, an FL-OFDC scheme for NNSs under external disturbances is developed to eliminate the offset, and its closed-loop stability criteria are derived. Finally, a chemical process network, that is, a specific case of IIoT, is employed to demonstrate the practicality of the FLPO and FL-OFDC methods.