Koopman Model Dimension Reduction via Variational Bayesian Inference and Graph Search

TL;DR

This paper introduces a hierarchical probabilistic approach using variational Bayesian inference and graph search to reduce the dimensionality of Koopman models, improving stability and prediction accuracy in control systems.

Contribution

It presents a novel Bayesian framework with inclusion flags and a graph search algorithm for effective Koopman model dimension reduction.

Findings

Reduced models maintain performance in experiments

Overcomes numerical instabilities

Effective state selection improves long-term predictions

Abstract

Koopman operator recently gained increasing attention in the control systems community for its abilities to bridge linear and nonlinear systems. Data driven Koopman operator approximations have established themselves as key enablers for system identification and model predictive control. Nonetheless, such methods commonly entail a preselected definition of states in the function space leading to high dimensional overfitting models and degraded long term prediction performances. We address this problem by proposing a hierarchical probabilistic approach for the Koopman model identification problem. In our method, elements of the model are treated as random variables and the posterior estimates are found using variational Bayesian (VB) inference updates. Our model distinguishes from others in the integration of inclusion flags. By the help of the inclusion flags, we intuitively threshold the probability of each state in the model. We then propose a graph search based algorithm to reduce the preselected states of the Koopman model. We demonstrate that our reduction method overcomes numerical instabilities and the reduced models maintain performance in simulated and real experiments.