714 research outputs found
A new kernel-based approach for overparameterized Hammerstein system identification
In this paper we propose a new identification scheme for Hammerstein systems,
which are dynamic systems consisting of a static nonlinearity and a linear
time-invariant dynamic system in cascade. We assume that the nonlinear function
can be described as a linear combination of basis functions. We reconstruct
the coefficients of the nonlinearity together with the first samples of
the impulse response of the linear system by estimating an -dimensional
overparameterized vector, which contains all the combinations of the unknown
variables. To avoid high variance in these estimates, we adopt a regularized
kernel-based approach and, in particular, we introduce a new kernel tailored
for Hammerstein system identification. We show that the resulting scheme
provides an estimate of the overparameterized vector that can be uniquely
decomposed as the combination of an impulse response and coefficients of
the static nonlinearity. We also show, through several numerical experiments,
that the proposed method compares very favorably with two standard methods for
Hammerstein system identification.Comment: 17 pages, submitted to IEEE Conference on Decision and Control 201
Identification of Stochastic Wiener Systems using Indirect Inference
We study identification of stochastic Wiener dynamic systems using so-called
indirect inference. The main idea is to first fit an auxiliary model to the
observed data and then in a second step, often by simulation, fit a more
structured model to the estimated auxiliary model. This two-step procedure can
be used when the direct maximum-likelihood estimate is difficult or intractable
to compute. One such example is the identification of stochastic Wiener
systems, i.e.,~linear dynamic systems with process noise where the output is
measured using a non-linear sensor with additive measurement noise. It is in
principle possible to evaluate the log-likelihood cost function using numerical
integration, but the corresponding optimization problem can be quite intricate.
This motivates studying consistent, but sub-optimal, identification methods for
stochastic Wiener systems. We will consider indirect inference using the best
linear approximation as an auxiliary model. We show that the key to obtain a
reliable estimate is to use uncertainty weighting when fitting the stochastic
Wiener model to the auxiliary model estimate. The main technical contribution
of this paper is the corresponding asymptotic variance analysis. A numerical
evaluation is presented based on a first-order finite impulse response system
with a cubic non-linearity, for which certain illustrative analytic properties
are derived.Comment: The 17th IFAC Symposium on System Identification, SYSID 2015,
Beijing, China, October 19-21, 201
Integrated Pre-Processing for Bayesian Nonlinear System Identification with Gaussian Processes
We introduce GP-FNARX: a new model for nonlinear system identification based
on a nonlinear autoregressive exogenous model (NARX) with filtered regressors
(F) where the nonlinear regression problem is tackled using sparse Gaussian
processes (GP). We integrate data pre-processing with system identification
into a fully automated procedure that goes from raw data to an identified
model. Both pre-processing parameters and GP hyper-parameters are tuned by
maximizing the marginal likelihood of the probabilistic model. We obtain a
Bayesian model of the system's dynamics which is able to report its uncertainty
in regions where the data is scarce. The automated approach, the modeling of
uncertainty and its relatively low computational cost make of GP-FNARX a good
candidate for applications in robotics and adaptive control.Comment: Proceedings of the 52th IEEE International Conference on Decision and
Control (CDC), Firenze, Italy, December 201
Regularized Nonparametric Volterra Kernel Estimation
In this paper, the regularization approach introduced recently for
nonparametric estimation of linear systems is extended to the estimation of
nonlinear systems modelled as Volterra series. The kernels of order higher than
one, representing higher dimensional impulse responses in the series, are
considered to be realizations of multidimensional Gaussian processes. Based on
this, prior information about the structure of the Volterra kernel is
introduced via an appropriate penalization term in the least squares cost
function. It is shown that the proposed method is able to deliver accurate
estimates of the Volterra kernels even in the case of a small amount of data
points
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