Online Real-time Learning of Dynamical Systems from Noisy Streaming Data: A Koopman Operator Approach

TL;DR

This paper introduces a robust, real-time algorithm based on Koopman operator theory for learning dynamical systems from noisy streaming data, enabling efficient monitoring and analysis.

Contribution

It presents a novel online learning algorithm that mitigates measurement noise using the Robust Koopman framework, improving speed and accuracy over existing methods.

Findings

Successfully identified Van der Pol oscillator dynamics

Efficiently analyzed the IEEE 68 bus power system

Demonstrated real-time monitoring of complex networks

Abstract

Recent advancements in sensing and communication facilitate obtaining high-frequency real-time data from various physical systems like power networks, climate systems, biological networks, etc. However, since the data are recorded by physical sensors, it is natural that the obtained data is corrupted by measurement noise. In this paper, we present a novel algorithm for online real-time learning of dynamical systems from noisy time-series data, which employs the Robust Koopman operator framework to mitigate the effect of measurement noise. The proposed algorithm has three main advantages: a) it allows for online real-time monitoring of a dynamical system; b) it obtains a linear representation of the underlying dynamical system, thus enabling the user to use linear systems theory for analysis and control of the system; c) it is computationally fast and less intensive than the popular Extended Dynamic Mode Decomposition (EDMD) algorithm. We illustrate the efficiency of the proposed algorithm by applying it to identify the Van der Pol oscillator, the IEEE 68 bus system, and a ring network of Van der Pol oscillators.