Personalized Federated Learning-Based Distributed Model Predictive Control With Predictive Error Compensation for Nonlinear Networked Systems

This paper develops a personalized federated learning-based distributed model predictive control (PFL-DMPC) method with predictive error compensation (PEC) for nonlinear networked systems with multiple subsystems to preserve data privacy and achieve the desired control performance despite the presence of modeling error of federated learning (FL) models. First, a personalized FL (PFL) algorithm is presented to obtain a global model using dynamic alternating iteration mode to update and aggregate personalized models, which preserves data privacy and addresses the heterogeneity issue among subsystems. Then, the convergence of the PFL algorithm with strongly convex property is proved, showing a faster convergence rate and higher computational efficiency than the existing FL algorithms. Next, since PFL models are integrated into a distributed model predictive control (DMPC) scheme, a DMPC scheme with PEC is developed to reduce the steady-state offset by incorporating the estimated prediction error into optimization problems. Finally, the simulation results for a nonlinear chemical process network demonstrate the convergence of the PFL algorithm and the superiority of the PFL-DMPC method with PEC compared to the PFL-DMPC method without accounting for model-plant mismatch. Note to Practitioners—This work addresses challenges in controlling nonlinear networked systems with multiple interconnected subsystems, particularly in ensuring privacy, managing heterogeneity, and compensating for prediction errors. These challenges often arise in industrial automation settings such as chemical processing, where subsystems exhibit diverse dynamics and data privacy is critical. We propose a PFL-DMPC framework with PEC. Unlike traditional centralized approaches, this PFL approach preserves data privacy by training models locally in each subsystems and sending them to a server to aggregate into a global model, thereby addressing subsystem-specific heterogeneity. The PEC mechanism corrects steady-state offsets caused by modeling inaccuracies, which ensures the system’s output aligns closely with desired trajectories. Practitioners can benefit from the faster convergence and improved adaptability of this framework, particularly in scenarios with limited communication bandwidth or data privacy concerns. However, implementing PFL-DMPC requires sufficient computational resources for iterative optimization and may demand fine-tuning of hyperparameters. Future work may explore extending this approach to real-time applications with stringent timing constraints. Potential applications include distributed control of multi-vehicle systems, smart grids, and robotic networks, where privacy-preserving and learning-based control is vital.