Authors:
Erik Weyer,
Marco C. Campi,
Volume: 1, Page 2688 Paper number 1382
Abstract:
In this paper we consider the finite sample properties of least squares
system identification, and we derive non-asymptotic confidence ellipsoids
for the estimate. Unlike asymptotic theory, the obtained confidence
ellipsoids are valid for a finite number of data points. The probability
that the estimate belongs to a certain ellipsoid has a natural dependence
on the volume of the ellipsoid, the data generating mechanism, the
model order and the number of data points available.
Authors:
Le Yi Wang,
Volume: 1, Page 2694 Paper number 1509
Abstract:
The relationship between information acquisition (identification)
and information processing (control) in their capability of dealing
with uncertainty is studied. It is revealed that such a relationship
can be established rigorously from the viewpoint of complexity. A
notion of information-based complexity is hence introduced, first
in its generality, and then in its special applications to metric spaces
in feedback control systems.
Authors:
Thomas E. Brehm,
Peter S. Maybeck,
Volume: 1, Page 2700 Paper number 1090
Abstract:
This paper investigates a generalization of the conventional approach
to LQG control design. First we investigate removing the assumption
that the Kalman filter as the observer is necessarily based on the
same model as the best plant model. The controller gain matrix design
is performed as usual, based on the optimal solution to the deterministic
design for the best model of the real-world plant. For the next case,
we also remove this controller design restriction to investigate robustness
to uncertainties in the plant model. The filter and controller gain
matrices are both determined by models possibly other than the plant
model. We relate the plant model to the filter and controller design
models by a position correlation (mean square error on output) measure
in order to determine optimal performance.
Authors:
Piet M.T. Broersen,
Stijn de Waele,
Volume: 1, Page 2706 Paper number 1425
Abstract:
A windowed and tapered periodogram can be computed as the Fourier
transform of an estimated covariance function of tapered data, multiplied
by a lag window. Covariances of finite length can also be modeled
as moving average (MA) time series models. The direct equivalence
between periodograms and MA models is shown in the method of moments
for MA estimation. A better MA representation for the covariance and
the spectral density is found with Durbin's improved MA method. That
uses the parameters of a long autoregressive (AR) model to find MA
models, followed by automatic selection of the MA order. A comparison
is made between the two MA model types. The best of many MA models
from windowed periodograms is compared to the single selected MA model
obtained with Durbin's method. The latter typically has a better
quality.
Authors:
Wei Xing Zheng,
Volume: 1, Page 2710 Paper number 1238
Abstract:
This paper is concerned with identification of stochastic linear systems
from noisy input and output measurements. A modified scheme that employs
extra delayed noisy measurements is derived to estimate the variances
of white input and output noises. These estimated noise variances are
then applied for removal of the bias from a least-squares parameter
estimate via an iterative procedure to achieve estimation consistency.
The new identification algorithm incorporated with this modified estimation
scheme for the noise variances demonstrates greatly improved performances.
Compared with the previously developed method, the new identification
algorithm can converge at a much faster rate and produce much more
accurate parameter estimates at only a slightly increased numerical
cost. The theoretical predictions are confirmed through Monte-Carlo
stochastic simulation studies.
Authors:
Soosan Beheshti,
Munther A. Dahleh,
Volume: 1, Page 2716 Paper number 1790
Abstract:
The problem of quantifying the error in estimation of low-complexity
models for stable linear time-invariant(LTI) systems is investigated.
We elaborate on the advantages of implementing a new method for order
selection of the model class.
|