49 research outputs found
An empirical Bayes approach to identification of modules in dynamic networks
We present a new method of identifying a specific module in a dynamic
network, possibly with feedback loops. Assuming known topology, we express the
dynamics by an acyclic network composed of two blocks where the first block
accounts for the relation between the known reference signals and the input to
the target module, while the second block contains the target module. Using an
empirical Bayes approach, we model the first block as a Gaussian vector with
covariance matrix (kernel) given by the recently introduced stable spline
kernel. The parameters of the target module are estimated by solving a marginal
likelihood problem with a novel iterative scheme based on the
Expectation-Maximization algorithm. Additionally, we extend the method to
include additional measurements downstream of the target module. Using Markov
Chain Monte Carlo techniques, it is shown that the same iterative scheme can
solve also this formulation. Numerical experiments illustrate the effectiveness
of the proposed methods
Bayesian kernel-based system identification with quantized output data
In this paper we introduce a novel method for linear system identification
with quantized output data. We model the impulse response as a zero-mean
Gaussian process whose covariance (kernel) is given by the recently proposed
stable spline kernel, which encodes information on regularity and exponential
stability. This serves as a starting point to cast our system identification
problem into a Bayesian framework. We employ Markov Chain Monte Carlo (MCMC)
methods to provide an estimate of the system. In particular, we show how to
design a Gibbs sampler which quickly converges to the target distribution.
Numerical simulations show a substantial improvement in the accuracy of the
estimates over state-of-the-art kernel-based methods when employed in
identification of systems with quantized data.Comment: Submitted to IFAC SysId 201
A new kernel-based approach to system identification with quantized output data
In this paper we introduce a novel method for linear system identification
with quantized output data. We model the impulse response as a zero-mean
Gaussian process whose covariance (kernel) is given by the recently proposed
stable spline kernel, which encodes information on regularity and exponential
stability. This serves as a starting point to cast our system identification
problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods
to provide an estimate of the system. In particular, we design two methods
based on the so-called Gibbs sampler that allow also to estimate the kernel
hyperparameters by marginal likelihood maximization via the
expectation-maximization method. Numerical simulations show the effectiveness
of the proposed scheme, as compared to the state-of-the-art kernel-based
methods when these are employed in system identification with quantized data.Comment: 10 pages, 4 figure
Kernel-based system identification from noisy and incomplete input-output data
In this contribution, we propose a kernel-based method for the identification
of linear systems from noisy and incomplete input-output datasets. We model the
impulse response of the system as a Gaussian process whose covariance matrix is
given by the recently introduced stable spline kernel. We adopt an empirical
Bayes approach to estimate the posterior distribution of the impulse response
given the data. The noiseless and missing data samples, together with the
kernel hyperparameters, are estimated maximizing the joint marginal likelihood
of the input and output measurements. To compute the marginal-likelihood
maximizer, we build a solution scheme based on the Expectation-Maximization
method. Simulations on a benchmark dataset show the effectiveness of the
method.Comment: 16 pages, submitted to IEEE Conference on Decision and Control 201
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