13 research outputs found
An Interpretation of the Dual Problem of the THREE-like Approaches
Spectral estimation can be preformed using the so called THREE-like approach.
Such method leads to a convex optimization problem whose solution is
characterized through its dual problem. In this paper, we show that the dual
problem can be seen as a new parametric spectral estimation problem. This
interpretation implies that the THREE-like solution is optimal in terms of
closeness to the correlogram over a certain parametric class of spectral
densities, enriching in this way its meaningfulness
Model Predictive Control meets robust Kalman filtering
Model Predictive Control (MPC) is the principal control technique used in
industrial applications. Although it offers distinguishable qualities that make
it ideal for industrial applications, it can be questioned its robustness
regarding model uncertainties and external noises. In this paper we propose a
robust MPC controller that merges the simplicity in the design of MPC with
added robustness. In particular, our control system stems from the idea of
adding robustness in the prediction phase of the algorithm through a specific
robust Kalman filter recently introduced. Notably, the overall result is an
algorithm very similar to classic MPC but that also provides the user with the
possibility to tune the robustness of the control. To test the ability of the
controller to deal with errors in modeling, we consider a servomechanism system
characterized by nonlinear dynamics
Robust Kalman Filtering under Model Perturbations
We consider a family of divergence-based minimax approaches to perform robust
filtering. The mismodeling budget, or tolerance, is specified at each time
increment of the model. More precisely, all possible model increments belong to
a ball which is formed by placing a bound on the Tau-divergence family between
the actual and the nominal model increment. Then, the robust filter is obtained
by minimizing the mean square error according to the least favorable model in
that ball. It turns out that the solution is a family of Kalman like filters.
Their gain matrix is updated according to a risk sensitive like iteration where
the risk sensitivity parameter is now time varying. As a consequence, we also
extend the risk sensitive filter to a family of risk sensitive like filters
according to the Tau-divergence family
Convergence analysis of a family of robust Kalman filters based on the contraction principle
In this paper we analyze the convergence of a family of robust Kalman
filters. For each filter of this family the model uncertainty is tuned
according to the so called tolerance parameter. Assuming that the corresponding
state-space model is reachable and observable, we show that the corresponding
Riccati-like mapping is strictly contractive provided that the tolerance is
sufficiently small, accordingly the filter converges
The Harmonic Analysis of Kernel Functions
Kernel-based methods have been recently introduced for linear system
identification as an alternative to parametric prediction error methods.
Adopting the Bayesian perspective, the impulse response is modeled as a
non-stationary Gaussian process with zero mean and with a certain kernel (i.e.
covariance) function. Choosing the kernel is one of the most challenging and
important issues. In the present paper we introduce the harmonic analysis of
this non-stationary process, and argue that this is an important tool which
helps in designing such kernel. Furthermore, this analysis suggests also an
effective way to approximate the kernel, which allows to reduce the
computational burden of the identification procedure
A new kernel-based approach for spectral estimation
The paper addresses the problem to estimate the power spectral density of an
ARMA zero mean Gaussian process. We propose a kernel based maximum entropy
spectral estimator. The latter searches the optimal spectrum over a class of
high order autoregressive models while the penalty term induced by the kernel
matrix promotes regularity and exponential decay to zero of the impulse
response of the corresponding one-step ahead predictor. Moreover, the proposed
method also provides a minimum phase spectral factor of the process. Numerical
experiments showed the effectiveness of the proposed method