Sparse Bayesian Learning for Koopman Based System Identification

Modeling nonlinear dynamical systems is important for control, prediction, and decision making in numerous engineering fields. While robust methods for identifying linear systems are well established, traditional approaches often struggle with complex nonlinear behavior, particularly when data is noisy or limited. Recently, the Koopman operator framework has gained popularity as it provides global linear representations of nonlinear systems, which enables the use of linear systems theory tools. However, existing data driven Koopman operator methods, such as extended dynamic mode decomposition (EDMD), can yield degraded performance under noisy conditions and typically require large amounts of training data. In this paper, we propose a new approach for learning Koopman models using sparse Bayesian learning (SBL). Our method identifies the beliefs over Koopman model parameters directly from model evidence while inherently promoting sparsity. Additionally, our approach demonstrates improved noise robustness and effective performance even with limited data. Unlike existing methods, the SBL approach provides valuable uncertainty quantification for the learned models, which is particularly beneficial for control applications requiring probabilistic performance guarantees.