  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.
