Online real-time learning of dynamical systems from noisy streaming data.

Area of Science:

• Dynamical Systems Theory
• Data Science
• Control Engineering

Background:

• High-frequency real-time data acquisition from physical systems is advancing.
• Measurement noise commonly corrupts sensor data, posing challenges for analysis.
• Existing methods like Extended Dynamic Mode Decomposition (EDMD) can be computationally intensive.

Purpose of the Study:

• To develop a novel algorithm for online, real-time learning of dynamical systems from noisy time-series data.
• To mitigate the impact of measurement noise on system identification.
• To provide a computationally efficient alternative to existing methods.

Main Methods:

• The proposed algorithm utilizes the Robust Koopman operator framework.
• It enables online, real-time monitoring and analysis of dynamical systems.
• The method achieves a linear representation of the system dynamics.

Main Results:

• The algorithm effectively mitigates measurement noise in time-series data.
• It provides a computationally faster and less intensive approach compared to EDMD.
• Successful identification of various systems including oscillators, chaotic maps, and power networks was demonstrated.

Conclusions:

• The novel algorithm offers efficient and robust online learning of noisy dynamical systems.
• Its linear representation facilitates the application of linear systems theory for analysis and control.
• The approach shows broad applicability across diverse physical systems.