Improved understanding of the loss-of-symmetry phenomenon in the conventional Kalman filter

This paper corrects an unclear treatment of the conventional Kalman filter implementation as presented by M. H. Verhaegen and P. van Dooren in Numerical aspects of different Kalman filter implementations, IEEE Trans. Automat. Contr., v. AC-31, no. 10, pp. 907-917, 1986. It is shown that habitual, incorrect implementation of the Kalman filter has been the major cause of its sensitivity to the so-called loss-of-symmetry phenomenon

A Bank of Reconfigurable LQG Controllers for Linear Systems Subjected to Failures

An approach for controller reconfiguration is presented. The starting point in the analysis is a sufficiently accurate continuous linear time-invariant (LTI) model of the nominal system. Based on a bank of reconfigurable LQG controllers, each designed for a particular combination of total faults, the reconfiguration consists of two operation modes. In the first mode a switching is invoked towards one of the pre-designed LQG controllers on the basis of the information about only the combination of total faults that is in effect. In the second mode, which is activated in cases of partial and component faults, a dynamic correction procedure is initiated which tries to reconfigure the currently active controller in such a way, that the failed closed-loop system remains stable and its performance is as close as possible to the performance of the closed-loop system with only total faults present in the system. In cases of partial faults the second mode is practically an extension of the modified pseudo-inverse method. In cases of component faults the second mode is based on an LMI optimization problem. The approach is illustrated using a model of a real-life space robot manipulator, in which total, partial and component faults are simulate

The minimal residual QR-factorization algorithm for reliably solving subset regression problems

A new algorithm to solve test subset regression problems is described, called the minimal residual QR factorization algorithm (MRQR). This scheme performs a QR factorization with a new column pivoting strategy. Basically, this strategy is based on the change in the residual of the least squares problem. Furthermore, it is demonstrated that this basic scheme might be extended in a numerically efficient way to combine the advantages of existing numerical procedures, such as the singular value decomposition, with those of more classical statistical procedures, such as stepwise regression. This extension is presented as an advisory expert system that guides the user in solving the subset regression problem. The advantages of the new procedure are highlighted by a numerical example

Round-off error propagation in four generally applicable, recursive, least-squares-estimation schemes

The numerical robustness of four generally applicable, recursive, least-squares-estimation schemes is analyzed by means of a theoretical round-off propagation study. This study highlights a number of practical, interesting insights of widely used recursive least-squares schemes. These insights have been confirmed in an experimental study as well

On the reliable and flexible solution of practical subset regression problems

A new algorithm for solving subset regression problems is described. The algorithm performs a QR decomposition with a new column-pivoting strategy, which permits subset selection directly from the originally defined regression parameters. This, in combination with a number of extensions of the new technique, makes the method a very flexible tool for analyzing subset regression problems in which the parameters have a physical meaning

The use of the QR factorization in the partial realization problem

The use of the QR factorization of the Hankel matrix in solving the partial realization problem is analyzed. Straightforward use of the QR factorization results in a realization scheme that possesses all of the computational advantages of Rissanen's realization scheme. These latter properties are computational efficiency, recursiveness, use of limited computer memory, and the realization of a system triplet having a condensed structure. Moreover, this scheme is robust when the order of the system corresponds to the rank of the Hankel matrix. When this latter condition is violated, an approximate realization could be determined via the QR factorization. In this second scheme, the given Hankel matrix is approximated by a low-rank non-Hankel matrix. Furthermore, it is demonstrated that column pivoting might be incorporated in this second scheme. The results presented are derived for a single input/single output system, but this does not seem to be a restriction

Comparison of two numerical techniques for aerodynamic model identification

An algorithm, called the Minimal Residual QR algorithm, is presented to solve subset regression problems. It is shown that this scheme can be used as a numerically reliable implementation of the stepwise regression technique, which is widely used to identify an aerodynamic model from flight test data. This capability as well as the numerical superiority of this scheme over the stepwise regression technique is demonstrated in an experimental simulation study

Blockwise Subspace Identification for Active Noise Control

In this paper, a subspace identification solution is provided for active noise control (ANC) problems. The solution is related to so-called block updating methods, where instead of updating the (feedforward) controller on a sample by sample base, it is updated each time based on a block of N samples. The use of the subspace identification based ANC methods enables non-iterative derivation and updating of MIMO compact state space models for the controller. The robustness property of subspace identification methods forms the basis of an accurate model updating mechanism, using small size data batches. The design of a feedforward controller via the proposed approach is illustrated for an acoustic duct benchmark problem, supplied by TNO Institute of Applied Physics (TNO-TPD), the Netherlands. We also show how to cope with intrinsic feedback. A comparison study with various ANC schemes, such as block filtered-U, demonstrates the increased robustness of a subspace derived controlle

LAPACK-Based Software for Subspace Identification

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