Online Real-time Learning of Dynamical Systems from Noisy Streaming Data: A Koopman Operator Approach
This work addresses the challenge of real-time system identification from noisy sensor data for applications like power networks and biological systems, offering an incremental improvement over prior Koopman-based methods.
The paper tackles the problem of learning dynamical systems from noisy streaming data by proposing a novel algorithm based on the Robust Koopman operator framework, which achieves online real-time monitoring, linear representation for analysis, and computational efficiency compared to existing methods like EDMD, as demonstrated on systems such as the Van der Pol oscillator and IEEE 68 bus system.
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.