Kalman Filter Aided Federated Koopman Learning

2025-07-07

AI Summary

To address practical challenges in real-time control and estimation of nonlinear systems—including unmeasurable states, sparse, low-quality, and decentralized observations—this paper proposes KF-FedKL, a deep Koopman learning framework integrating the Unscented Kalman Filter (UKF) with federated learning. KF-FedKL is the first to jointly embed UKF, the Unscented Rauch–Tung–Striebel smoother, and a modified FedAvg algorithm into an end-to-end federated Koopman neural network, enabling privacy-preserving, collaborative linearization modeling across multiple clients. Unlike conventional approaches, KF-FedKL requires no precise prior knowledge of system states and achieves high-accuracy state estimation and Koopman operator learning solely from local sparse observations. Theoretical analysis establishes its convergence, while extensive numerical experiments demonstrate its robustness and effectiveness under varying noise levels and data missingness scenarios.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Intelligent Robots: State Estimation
• Search and Optimization: Learning to Search

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Real-time control and estimation are pivotal for applications such as industrial automation and future healthcare. The realization of this vision relies heavily on efficient interactions with nonlinear systems. Therefore, Koopman learning, which leverages the power of deep learning to linearize nonlinear systems, has been one of the most successful examples of mitigating the complexity inherent in nonlinearity. However, the existing literature assumes access to accurate system states and abundant high-quality data for Koopman analysis, which is usually impractical in real-world scenarios. To fill this void, this paper considers the case where only observations of the system are available and where the observation data is insufficient to accomplish an independent Koopman analysis. To this end, we propose Kalman Filter aided Federated Koopman Learning (KF-FedKL), which pioneers the combination of Kalman filtering and federated learning with Koopman analysis. By doing so, we can achieve collaborative linearization with privacy guarantees. Specifically, we employ a straightforward yet efficient loss function to drive the training of a deep Koopman network for linearization. To obtain system information devoid of individual information from observation data, we leverage the unscented Kalman filter and the unscented Rauch-Tung-Striebel smoother. To achieve collaboration between clients, we adopt the federated learning framework and develop a modified FedAvg algorithm to orchestrate the collaboration. A convergence analysis of the proposed framework is also presented. Finally, through extensive numerical simulations, we showcase the performance of KF-FedKL under various situations.

Problem

• Real-time control in nonlinear systems with limited data
• Privacy-preserving collaborative Koopman linearization
• Accurate system estimation from noisy observations

Innovation

• Combines Kalman filtering with federated learning
• Uses deep Koopman network for system linearization
• Ensures privacy via modified FedAvg algorithm