871 research outputs found
A kernel method for non-linear systems identification β infinite degree volterra series estimation
Volterra series expansions are widely used in analyzing
and solving the problems of non-linear dynamical
systems. However, the problem that the number of
terms to be determined increases exponentially with the
order of the expansion restricts its practical application.
In practice, Volterra series expansions are truncated
severely so that they may not give accurate representations
of the original system. To address this problem,
kernel methods are shown to be deserving of exploration.
In this report, we make use of an existing result
from the theory of approximation in reproducing kernel
Hilbert space (RKHS) that has not yet been exploited in
the systems identification field. An exponential kernel
method, based on an RKHS called a generalized Fock
space, is introduced, to model non-linear dynamical systems
and to specify the corresponding Volterra series
expansion. In this way a non-linear dynamical system
can be modelled using a finite memory length, infinite
degree Volterra series expansion, thus reducing the
source of approximation error solely to truncation in
time. We can also, in principle, recover any coefficient
in the Volterra series
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