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Jean-François Magni
ONERA - Toulouse
CERT-DCSD-IDCO
BP 4025
F-31055 Toulouse Cedex 04
France

Jean-François left us on January 4th, 2008. You can read the obituary which will be published soon in the European Journal of Control, and also the letter adressed by President Denis Maugars to Onera personnel delegates (in French).

BOOKS

TOOLBOXES

Education

Master of Sciences of Imperial College, London, UK (1979)
Docteur of SUPAERO, Toulouse, France (1981)
Docteur es Sciences of Université Paul Sabatier, Toulouse (1987)

Fields of interest

µ-Analysis.

Available standard tools for µ-analysis are not very efficient for dealing with non-academic problems: First, algorithms for µ lower bound computation relative to uncertain systems only depending on real uncertain parameters (such tools are really needed in industry) have too erratic convergence properties. In addition, the standard regularization which consists of adding artificial complex uncertainties in order to improve convergence, lead to approximate results that cannot always be interpreted (flexible systems). Second, for flexible systems (i.e. systems characterized by very narrow peaks of the µ-curve), a very (too) tight frequency girding is required. Available frequency sweeping techniques cannot be efficiently applied when the number of system states is larger than about twenty.

Lower bounds of µ in the case of real uncertainties. We have proposed two algorithms based on pole assignment: the matrix of uncertainties is considered as a feedback gain for pole assignment. Computing a lower bound consists of finding the smallest amount of uncertainties which "assign" a pole on the imaginary axis. These techniques are iterative but convergence appeared to be good for all considered systems.
Upper bounds without frequency girding. In order to use continuous frequency sweeping (instead of considering the frequency as an additional artificial uncertain parameter inducing very complex LMIs), we propose to use the standard scaling matrices (D,G) on a frequency interval instead of at the fixed frequency where they were computed. The resulting LMI are of same complexity as in the frequency girding case.

The combination of our lower and upper bound tools applied to the stability analysis of a satellite received the Best Application Paper prize at the IFAC World Congress of Beijing (1999). A summary of our contribution is available on line : Mu-analysis for flexible systems.

LFT-modelling.

It is in principle very easy to compute LFT models of uncertain systems. Unfortunately the most straightforward techniques lead to very high order models. For robustness analysis and for feedback design, low order LFT models are required. For this reason I developed (2001) a Matlab toolbox with special emphasis on order reduction and approximation. This toolbox considers object-oriented techniques and/or symbolic approaches. More details: reports, toolbox. Version 2 of the toolbox (2006) introduces a more advanced LFT object. It is co-authored with S. Hecker and A. Vargas (see here). It is also available for Scilab.

Robust control design.

For robust control design I use a multi-model approach. Basically, I suggest to alternate analysis in order to detect worst cases and multi-model control design in order to control all together the detected worst cases. The advantage of such an approach to robustness is the lack of conservatism in the case of real uncertainties (the counter part is that the speed of variation of uncertain parameters is ignored). Using LFTs / µ-analysis it can be checked that the design relative to the treated worst cases is also okay for the continuum of models to be dealt with. The disadvantage (but only for publications!) is that we cannot prove a priori that this process converges, in practice, two or three steps are usually sufficient. The technique I propose for multi-model control design, consists of solving a LQ Programming or an LMI problem (convex optimization, very fast in the LQP case) at each step. The corresponding tools (LQP approach) are available in the following Matlab / Scilab toolboxes.

Gain scheduling.

Gain scheduling in LFT-form is a natural extension to modelling in LFT-form. A feedback gain in LFT-form is a kind of scheduled gain. Combining this approach with robust multimodel control (as above) permits us to treat simultaneously

scheduling with respect to measured parameters (measured parameters of the LFT model)
robustness with respect to uncertain parameters (other parameters of the LFT model).

See the tutorial section for a introduction to LFT gain design.

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