  In this paper, we provide an algorithm for online computation of Koopman
operator in real-time using streaming data. In recent years, there has been an
increased interest in data-driven analysis of dynamical systems, with operator
theoretic techniques being the most popular. Existing algorithms, like Dynamic
Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD), use
the entire data set for computation of the Koopman operator. However, many real
life applications like power system analysis, biological systems, building
systems etc. requires the real-time computation and updating of the Koopman
operator, as new data streams in. In this paper, we propose an iterative
algorithm for online computation of Koopman operator such that at each time
step the Koopman operator is updated incrementally. In particular, we propose a
Recursive Extended Dynamic Decomposition (rEDMD) algorithm for computation of
Koopman operator from streaming data. Further, we test the algorithm in three
different dynamical systems, namely, a linear system, a nonlinear system and a
system governed by a Partial Differential Equation (PDE) and illustrate the
computational efficiency of the iterative algorithm over the existing DMD and
EDMD algorithms.
