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<title>Five most publications of Ivan Markovsky</title>
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<h1>Five most publications of Ivan Markovsky</h1>
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[<a name="M07">1</a>]
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I. Markovsky.
Structured low-rank approximation and its applications.
<em>Automatica</em>, 44(4):891-909, 2008.
[ <a href="http://dx.doi.org/10.1016/j.automatica.2007.09.011">DOI</a> |
<a href="http://eprints.soton.ac.uk/263379/9/slra_published.pdf">.pdf</a> ]
<blockquote>
Fitting data by a bounded complexity linear model is equivalent to low-rank approximation of a matrix constructed from the data. The data matrix being Hankel structured is equivalent to the existence of a linear time-invariant system that fits the data and the rank constraint is related to a bound on the model complexity. In the special case of fitting by a static model, the data matrix and its low-rank approximation are unstructured.<p>
We outline applications in system theory (approximate realization, model reduction, output error and errors-in-variables identification), signal processing (harmonic retrieval, sum-of-damped exponentials and finite impulse response modeling), and computer algebra (approximate common divisor). Algorithms based on heuristics and local optimization methods are presented. Generalizations of the low-rank approximation problem result from different approximation criteria (e.g., weighted norm) and constraints on the data matrix (e.g., nonnegativity). Related problems are rank minimization and structured pseudospectra.
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[<a name="MR07">2</a>]
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I. Markovsky and P. Rapisarda.
Data-driven simulation and control.
<em>Int. J. Control</em>, 81(12):1946-1959, 2008.
[ <a href="http://dx.doi.org/10.1080/00207170801942170">DOI</a> |
<a href="http://eprints.soton.ac.uk/263423/">http</a> |
<a href="http://eprints.soton.ac.uk/263423/1/ddctr.pdf">.pdf</a> ]
<blockquote>
Classical linear time-invariant system simulation methods are based on a transfer function, impulse response, or input/state/output representation. We present a method for computing the response of a system to a given input and initial conditions directly from a trajectory of the system, without explicitly identifying the system from the data. Similarly to the classical approach for simulation, the classical approach for control is model-based: first a model representation is derived from given data of the plant and then a control law is synthesised using the model and the control specifications. We present an approach for computing a linear quadratic tracking control signal that circumvents the identification step. The results are derived assuming exact data and the simulated response or control input is constructed off-line.
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[<a name="MPV04a">3</a>]
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I. Markovsky, J. C. Willems, S. Van Huffel, B. De Moor, and R. Pintelon.
Application of structured total least squares for system
identification and model reduction.
<em>IEEE Trans. Automat. Control</em>, 50(10):1490-1500, 2005.
[ <a href="http://dx.doi.org/10.1109/TAC.2005.856643">DOI</a> |
<a href="http://eprints.ecs.soton.ac.uk/13300/1/stls_appl_published.pdf">.pdf</a> ]
<blockquote>
The following identification problem is considered: minimize the <em>l</em><sub>2</sub> norm of the difference between a given time series and an approximating one under the constraint that the approximating time series is a trajectory of a linear time invariant system of a fixed complexity. The complexity is measured by the input dimension and the maximum lag. The question leads to a problem that is known as the global total least squares problem and alternatively can be viewed as maximum likelihood identification in the errors-in-variables setup. Multiple time series and latent variables can be considered in the same setting. Special cases of the problem are autonomous system identification, approximate realization, and finite time optimal <em>l</em><sub>2</sub> model reduction. <p>
The identification problem is related to the structured total least squares problem. The paper presents an efficient software package that implements the theory. The proposed method and software are tested on data sets from the database for the identification of systems DAISY.
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[<a name="MWRDM04">4</a>]
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I. Markovsky, J. C. Willems, P. Rapisarda, and B. De Moor.
Algorithms for deterministic balanced subspace identification.
<em>Automatica</em>, 41(5):755-766, 2005.
[ <a href="http://dx.doi.org/10.1016/j.automatica.2004.10.007">DOI</a> |
<a href="http://eprints.soton.ac.uk/262202/">http</a> |
<a href="http://eprints.soton.ac.uk/262202/1/AutomaticaSubspaceID.pdf">.pdf</a> ]
<blockquote>
New algorithms for identification of a balanced state space representation are proposed. They are based on a procedure for estimation of the impulse response and sequential zero input responses directly from data. The proposed algorithms are more efficient than the existing alternatives that compute the whole Hankel matrix of Markov parameters. It is shown that the computations can be performed on Hankel matrices of the input-output data of various dimensions. By choosing wider matrices, we need persistency of excitation of smaller order. Moreover, this leads to computational savings and improved statistical accuracy when the data is noisy. Using a finite amount of input-output data, the existing algorithms compute finite time balanced representation and the identified models have a lower bound on the distance to an exact balanced representation. The proposed algorithm can approximate arbitrarily closely an exact balanced representation. Moreover, the finite time balancing parameter can be selected automatically by monitoring the decay of the impulse response. We show what is the optimal in terms of minimal identifiability condition partition of the data into “past” and “future”.
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[<a name="book">5</a>]
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I. Markovsky, J. C. Willems, S. Van Huffel, and B. De Moor.
<em>Exact and Approximate Modeling of Linear Systems: A Behavioral
Approach</em>.
Number 11 in Monographs on Mathematical Modeling and Computation.
SIAM, March 2006.
[ <a href="http://dx.doi.org/10.1137/1.9780898718263">DOI</a> |
<a href="http://homepages.vub.ac.be/~imarkovs/siam-book.pdf">.pdf</a> ]
<blockquote>
The book introduces the behavioral approach to mathematical modeling, an approach that requires models to be viewed as sets of possible outcomes rather than to be a priori bound to particular representations. Linear, bilinear, and quadratic static models and linear dynamic models are considered. The book presents exact subspace-type and approximate optimization-based identification methods, as well as representation-free problem formulations, an overview of solution approaches, and software implementation. The presented theory leads to algorithms that are implemented in C language and in MATLAB.
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</table><hr><p><em>This file was generated by
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