| 1. |
- Henrion, Didier, et al.
(author)
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Reduced LMIs for Fixed-Order Polynomial Controller Design
- 2004
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In: Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems. - 9056825178
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Conference paper (peer-reviewed)abstract
- A reduction procedure based on semidefinite programming duality is applied to LMI conditions for fixed-order scalar linear controller design in the polynomial framework. It is namely shown that the number of variables in the reduced design LMI is equal to the difference between the open-loop plant order and the desired controller order. A standard linear system of equations must then be solved to retrieve the controller parameters. Therefore high computational load is not necessarily expected when the number of controller parameters is large, but rather when a large number of plant parameters are to be controlled with a small number of controller paramters. Tailored interior-point algorithms dealing with the specific structure of the reduced design LMI are also discussed.
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| 2. |
- Iftime, Orest, et al.
(author)
-
A Grassmanian Approach to the Hankel Norm Approximation Problem
- 2004
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In: Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems, Leuven, Belgium.
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Conference paper (peer-reviewed)abstract
- This paper concerns the unifying framework to strictly contractive extension problems, which is usually referred to as the band method. The solution to the so-called strictly contractive extension problem in this abstract framework, when applied to a certain concrete case, yields a complete characterization of solutions to the sub-optimal Nehari problem. The sub-optimal Hankel norm approximation problem is a more general problem, which is closely related to the model reduction problem in control theory. It covers the Nehari problem as a special case, but does not fit into the existing abstract framework. This problem is addressed in the present paper. In this paper the Grassmannian version of the band method is suitable enlarged so as to include the sub-optimal Hankel norm approximation problem as a special case as well. Our abstract result is illustrated on two concrete problems, one for time-invariant infinite dimensional systems and the other for time-variant periodic finite dimensional systems.
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| 3. |
- Rantzer, Anders
(author)
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l2 gain bounded adaptive control of a first order linear system
- 2004
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In: Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS). - 9056825178
-
Conference paper (peer-reviewed)abstract
- The problem of adaptive control is considered from a perspective of l2-gain. It has recently been shown that without an a priori bound on the system parameters, there exists no single dynamic feedback law that achieves bounded gain from disturbances to state for all first order linear systems. In this paper, a converse statement is proved for a standard adaptive scheme where the parameter estimate is saturated at a prespecified level. It is proved that the l2-gain with this controller grows at most linearly with the size of the a priori bound on the unknown parameter.
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