On Recursive Proper Orthogonal Decomposition Methods and Applications to Distributed Sensing in Cyber-Physical Systems
C. Xu, L. Luo and E. Schuster
American Control Conference
Baltimore, Maryland, USA, June 30 - July 2, 2010
Abstract
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Distributed sensing of cyber-physical systems has become feasible
with recent developments in sensor technology, wireless communication
and distributed computing. Distributed sensing generates huge amounts
of data from the events occurring in the physical side, which should
be promptly reflected in the cyber side so that actions can be made
timely by the computing systems. Due to the dense temporal-spatial
distribution of the measured data, great challenges have been posed
in terms of data storage, information processing and communications.
The proper orthogonal decomposition (POD) method is a powerful tool
to extract dominant information from distributed observational data,
which has been widely used in signal processing and pattern analysis
of fluid turbulence. The classical POD method implements dominant
information extraction when the entire data set is known. However, in
real- time measurements, new data is collected and incorporated into
the historic data set at each sampling time. We propose a recursive
proper orthogonal decomposition (rPOD) method based on the operator
perturbation theory, where the accumulative truncation error can be
controlled by a gradient search algorithm. This method is illustrated
with two state-of-the-art problems governed by the heat conduction
equation (1D) and the Navier-Stokes equations (2D) respectively.